Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

L’étude de la structure de l’ARN est reconnue un sujet d’actualité qui permet de connaître sa fonction. Il existe différentes techniques enzymatiques ou chimiques classiques et récentes couplées au séquençage à haut débit pour étudier la structure de l’ARN. Le projet de thèse vise l’optimisation de deux techniques de cartographie déjà existantes et se divise en deux parties. La première partie concerne l’optimisation de la technique de hSHAPE et ceci en synthétisant de nouvelles sondes fluorescentes à transfert d’énergie capables d’étudier de faibles quantités d’ARN et adaptées au séquenceur d’ADN. Mon travail a permis la synthèse de 5 molécules fluorescentes intermédiaires et l’obtention d’une sonde finale. L’étude de cette sonde a montrée que l’interaction entre les deux fluorophores est majoritairement due à un mécanisme de couplage excitonique causé par la flexibilité et la distance entre les deux entités fluorescentes. De plus, les propriétés de la molécule sont fortement dépendantes du solvant. Dans la deuxième partie, nous cherchons à optimiser la cartographie en solution afin d’étudier le génome entier du VIH-1 in virio. Pour cela, nous avons synthétisé 4 molécules dérivées de l’anhydride isatoïque et modifiées sur la fonction amine N1 par un groupement propyn-2-yle. Nous avons aussi préparé 8 molécules de référence. De plus, des études préliminaires réalisées sur l’ARN 1-311 du VIH-1 ont montré que nos composés modifient l’ARN et qu’il est possible de fixer la biotine-PEG3-azoture par click chemistry sur les ARN ainsi modifiés. / Understanding the function of RNA involved in biological processes requires a thorough knowledge of RNA structure. Traditional chemical and enzymatic reagents and backbonebased cleavage are useful for mapping RNA secondary structure, and on going advances in nucleotide resolution RNA structure probing have made possible increasingly rigorous and quantitative analysis. Although chemical and enzymatic probes are recently coupled to high throughput sequencing, these techniques still suffer from some disadvantages. This project aims the optimization of two existing techniques and is divided into two major topics. The first part aims the optimization of “hSHAPE chemistry”. A practical method is the synthesis of energy transfer dyes from the “BigDyes” family that are useful to study small amount of RNA and are compatible with DNA sequencing. We have done the synthesis of 5 modified dyes and one BigDye. The characterization of this BigDye shows that it exists excitoncoupling mechanism due to the strong interaction between the two transition dipoles. In addition, the solvent influences strongly the photophysical properties of this BigDye. The purpose of the second part is to develop and synthesize new class of isatoic anhydride derivatives useful to map the entire genome of HIV-1 in virio. We have done the synthesis of 4 N-substituted molecules with a propyn-2-yl function and 8 reference molecules. In addition, preliminary results on HIV-1 1-311 RNA showed that these compounds are able to modify RNA and that it is possible to fix a biotin-azide by click chemistry.

La pratique contractuelle des prestataires de services d'investissements s'illustre tant à l'occasion de la fourniture des services d'investissement que lors de montage contractuel issu de la pratique. L'objet de cette étude est de cerner quelles sont les nouvelles règles d'ordre public susceptibles de mettre à mal la sécurité juridique des PSI à l'occasion de cette pratique contractuelle. / Contractual practice of providers of investment illustrates both the provision of investment services and contract assembly created by the practice . The purpose of this study is to identify what are the new public order rules that undermine the legal certainty of PSI during this contractual practice.

We investigate the famous Laguerre–Pólya class of entire functions and its subclass, the Laguerre–Pólya class of type I. The functions from these classes can be expressed in terms of the Hadamard Canonical Factorization (see Chapter 1, Definition 1.2 and 1.3). The prominent theorem by E. Laguerre and G. Pólya gives a complete description of the Laguerre–Pólya class and the Laguerre–Pólya class of type I, showing that these classes are the respective closures in the topology of uniform convergence on compact sets of the set of real polynomials having only real zeros (that is, the set of so-called hyperbolic polynomials) and the set of real polynomials having only real negative zeros. Both the Laguerre–Pólya class and the Laguerre–Pólya class of type I play an essential role in complex analysis. For the properties and characterizations of these classes, see, for example, [31] by A. Eremenko, [40] by I.I. Hirschman and D.V. Widder, [43] by S. Karlin, [57] by B.Ja. Levin, [66, Chapter 2] by N. Obreschkov, and [74] by G. Pólya and G. Szegö. In the thesis, we study entire functions with positive coefficients and with the monotonic sequence of their second quotients of Taylor coefficients. We find necessary and sufficient conditions under which such functions belong to the Laguerre–Pólya class (or the Laguerre–Pólya class of type I).:List of symbols Introduction 1 Background of research 1 1.1 The Laguerre–Pólya class .................... 1 1.2 The quotients of Taylor coefficients ............... 3 1.3 Hutchinson’s constant ...................... 4 1.4 Multiplier sequences ....................... 4 1.5 Apolar polynomials........................ 8 1.6 The partial theta function .................... 10 1.7 Decreasing second quotients ................... 13 1.8 Increasing second quotients ................... 14 2 A necessary condition for an entire function with the increasing second quotients of Taylor coefficients to belong to the Laguerre–Pólya class 15 2.1 Proof of Theorem 2.1....................... 16 2.2 The q-Kummer function ..................... 29 2.3 Proof of Theorem 2.10 ...................... 31 2.4 Proof of Theorem 2.11 ...................... 43 3 Closest to zero roots and the second quotients of Taylor coefficients of entire functions from the Laguerre–Pólya I class 49 3.1 Proof of Statement 3.1 ...................... 50 3.2 Proof of Theorem 3.2....................... 53 3.3 Proof of Theorem 3.4....................... 61 3.4 Proof of Theorem 3.6....................... 66 4 Entire functions from the Laguerre–Pólya I class having the increasing second quotients of Taylor coefficients 69 4.1 Proof of Theorem 4.1....................... 70 4.2 Proof of Theorem 4.3....................... 76 5 Number of real zeros of real entire functions with a non-decreasing sequence of the second quotients of Taylor coefficients 81 5.1 Proof of Theorem 5.1....................... 82 5.2 Proof of Corollary 5.2....................... 88 5.3 Proof of Theorem 5.4....................... 88 6 Further questions 95 Acknowledgements 97 Selbständigkeitserklärung 101 Curriculum Vitae 103 Bibliography 107

This thesis examines five religious organisations which existed in the Canadian provinces of New Brunswick, Nova Scotia and Prince Edward Island, collectively known as the Maritime Region, between 1880 and 1920. Each of these denominations emphasised holiness theology, albeit in varying degrees. They include, in order of their establishment in the region, the Methodist Church, the Free Christian Baptist Conference, the Salvation Army, the Reformed Baptist Alliance of Canada and the Pentecostal Church of the Nazarene. This study assesses these religious bodies in a number of ways. First, it examines their theological beliefs, comparing them with one another and tracing any changes which occurred in them between 1880 and 1920. Second, it considers the various associations which each of these denominations developed with the late nineteenth-century American holiness movement. The enquiry devotes particular attention to the response of each religious body to a spiritual encounter, known as ‘entire instantaneous sanctification’, popularised especially during the last quarter of the nineteenth century by the holiness movement in parts of Canada, Great Britain and the United States. Third, a review of the unique strengths and weaknesses of each of the five institutions offers an explanation for the numerical and financial growth of several of these groups early in the twentieth century, as well as the degeneration of others. Fourth, the study discloses much of the opposition which was directed towards Maritime holiness movement sympathisers, offering a number of explanations why some of these individuals left their traditional religious affiliations to join holiness bodies which they perceived to be true advocates of scriptural holiness. Fifth, it appraises the strong leadership which a number of individuals offered to the holiness cause in the Maritime region, taking into account the education, religious training, financial status, gender and ancestral origin of these men and women. Finally, a thorough statistical analysis of each constituency highlights the unique composition of each denomination’s membership. Taken together, these features inform the primary argument of the thesis, which is that significant transformations occurred in some of these religious bodies at the same time as large percentages of constituents became wealthier and more socially acceptable. These changes eventually facilitated the merger of the Methodist Church and the Free Christian Baptist Conference, the two oldest denominations, with national mainline religious bodies. This thesis contends that such unions may not have occurred had these groups not attained public recognition. Furthermore, in realising these achievements both of these denominations relinquished the more radical elements of their heritage, as well as much of the spiritual passion linked with it.

Soit P(z):=\sum_{\nu=0}^na_\nu z^{\nu}$ un polynôme de degré n et M:=\sup_{|z|=1}|P(z)|.$ Sans aucne restriction suplémentaire, on sait que $|P'(z)|\leq Mn$ pour $|z|\leq 1$ (inégalité de Bernstein). Si nous supposons maintenant que les zéros du polynôme $P$ sont à l'extérieur du cercle $|z|=k,$ quelle amélioration peut-on apporter à l'inégalité de Bernstein? Il est déjà connu [{\bf \ref{Mal1}}] que dans le cas où $k\geq 1$ on a $$(*) \qquad |P'(z)|\leq \frac{n}{1+k}M \qquad (|z|\leq 1),$$ qu'en est-il pour le cas où $k < 1$? Quelle est l'inégalité analogue à $(*)$ pour une fonction entière de type exponentiel $\tau ?$ D'autre part, si on suppose que $P$ a tous ses zéros dans $|z|\geq k \, \, (k\geq 1),$ quelle est l'estimation de $|P'(z)|$ sur le cercle unité, en terme des quatre premiers termes de son développement en série entière autour de l'origine. Cette thèse constitue une contribution à la théorie analytique des polynômes à la lumière de ces questions. / Let P(z):=\sum_{\nu=0}^na_\nu z^{\nu}$ a polynomial of degree n and M:=\sup_{|z|=1}|P(z)|$. Without any additional restriction, we know that $|P '(z) | \leq Mn$ for $| z | \leq 1$ (Bernstein's inequality). Now if we assume that the zeros of the polynomial $P$ are outside the circle $| z | = k$, which improvement could be made to the Bernstein inequality? It is already known [{\bf \ref{Mal1}}] that in the case where $k \geq 1$, one has$$ (*) \qquad | P '(z) | \leq \frac{n}{1 + k} M \qquad (| z | \leq 1),$$ what would it be in the case where $k < 1$? What is the analogous inequality for an entire function of exponential type $\tau$? On the other hand, if we assume that $P$ has all its zeros in $| z | \geq k \, \, (k \geq 1),$ which is the estimate of $| P '(z) |$ on the unit circle, in terms of the first four terms of its Maclaurin series expansion. This thesis comprises a contribution to the analytic theory of polynomials in the light of these problems.

O bocavirus humano (HBoV) é um parvovirus recentemente identificado em associação com a presença de sintomas de infecção do trato respiratório. Esse vírus possui um genoma de aproximadamente 5217 nucleotídeos que contém 3 open reading frames que codificam 4 proteínas (NS1, NP-1, VP-1 e VP-2). HBoV tem sido detectado em amostras respiratórias de diversas partes do mundo, incluindo Austrália, América do Norte, Europa, Ásia e África, o que sugere uma distribuição global desse vírus. Entretanto, nenhum estudo longitudinal de HBoV em amostras respiratórias foi realizado na América Latina. Dessa forma, nós realizamos um estudo prospectivo de HBoV em lavados nasofaríngeos (LFNs) coletados de pacientes com sintomas de infecção do trato respiratório (IRA) atendidos em um hospital universitário de Ribeirão Preto, SP e em um hospital universitário de Salvador, BA no período entre 2005 a 2007. 1288 LFNs de 1217 pacientes foram encaminhados ao laboratório de virologia e foram testados por PCR para HBoV. Desses pacientes, 962 eram menores de 5 anos e 177 eram maiores de 5 anos. Além disso, também foram analisados 50 LFNs de crianças menores de 5 anos que não tinham sintomas respiratórios. Todas as amostras positivas para HBoV foram testadas para todos os outros vírus respiratórios, incluindo o vírus sincicial respiratório (HRSV), rinovirus humano (HRV), influenza humano (HFLU), metapneumovirus humano (HMPV), parainfluenza humano (HPIV), coronavirus humano (HCoV) e adenovirus humano (HAdV). A carga viral de HBoV foi determinada por PCR em tempo real em todas as amostras positivas e o genoma completo de 19 amostras de HBoV foi seqüenciado. Com intuito, de fazer um levantamento sorológico e determinar sítios replicativos de HBoV, nós ainda clonamos e expressamos em S. cerevisae (Y258) o gene de VP2, que codifica uma das proteínas do capsídeo viral. A prevalência desse vírus foi de 4,8% em crianças menores de cinco anos e de 1% em pacientes maiores de cinco anos. HBoV não foi detectado em crianças sem sintomas. Dos 259 pacientes analisados em 2005, 25 (10%) foram positivos para HBoV. Esse vírus circulou mais frequentemente em abril, mês de maior incidência do HRSV. Em 2006, HBoV foi detectado em apenas 10 LFNs de 334 (3%) amostras testadas, sem qualquer pico de freqüência. Em 2007 HBoV foi detectado em 13 de 552 (2%) amostras, com uma freqüência de detecção um pouco maior em junho e julho. Os sintomas mais comumente observados foram rinorréia, tosse, febre e chiado, que foram observados geralmente em mais de 50% dos casos positivos para HBoV. Não houve uma diferença significativa na prevalência desses sintomas entre as crianças positivas e negativas para HBoV. Entretanto, foi observada uma maior freqüência de diarréia entre as crianças com esse vírus. Nesse estudo também foi documentado uma alta freqüência de co-infecções virais entre os pacientes com HBoV. Os vírus mais frequentemente associados com o bocavirus humano foram: HRSV, HRV e HAdV. Além disso, foi detectado uma maior carga viral media e uma maior freqüência de diarréia nos 15 pacientes com infecção exclusiva por HBoV do que nos pacientes com co-infecção. Esses resultados mostraram que HBoV pode alcançar títulos enormes (tão grandes como1014/mL) em LFNs de pacientes com sintomas respiratórios e que isso é associado a de diarréia. O seqüenciamento do genoma inteiro de HBoV realizado nesse estudo indica que a divergência genômica entre as amostras desse vírus é muito pequena. Como conclusão, nós demonstramos que HBoV circula e é detectado em associação com sintomas de infecção respiratória e diarréia no Brasil. Novos estudos, com um longo acompanhamento em diferentes populações serão necessários para determinar a sazonalidade e o real impacto clínico de HBoV em nosso país. / Human bocavirus (HBoV) is a parvovirus recently identified in association with respiratory tract infections. HBoV 5217 nt genome contains 3 open reading frames encoding four proteins (NS1, NP-1, VP-1 and VP-2). HBoV has been reported in respiratory samples from children in several parts of the world (including Australia, North America, Europe, Asia, and Africa), suggesting that the virus circulates worldwide. However, no longitudinal studies of HBoV in respiratory samples have been reported in Latin America. We report a prospective study of HBoV in nasopharyngeal aspirates (NPAs) collected from patients seen for acute respiratory tract infections (ARI) at the University of Sao Paulo Hospital in Ribeirao Preto, southeast Brazil and at the University Hospital in Salvador, Brazil. 1288 NPAs from 1217 patients was submitted to the virology lab for respiratory virus detection from 2005 to 2007 and were screened for HBoV by polymerase chain reaction (PCR), whom 962 were under 5 years of age and 177 were older than 5 years. In addition, NPAs from 50 children under 12 years without IRA was also tested to HBoV for PCR. All samples positive of HBoV was tested for others respiratory virus, including the human respiratory syncitial virus (HRSV), human rhinovirus (HRV), human influenza (HFLU), human metapneumovirus (HMPV), human parainfluenza virus (HPIV), human coronavirus (HCoV) and human adenovirus (HAdV). These samples had their HBoV viral load determined by real time PCR and the viral entire genome of nineteen HBoV sample was sequenced. We also cloned and expressed in S. cerevisae (Y258) the gene of VP2, one protein of viral capside. The prevalence of this virus was of 4,8% in children under 5 years and 1% in adults, both with IRA. HBoV was not found on the patients without symptoms. In 2005, of the 259 patients tested, 25 (10%) were positive for HBoV. Interestingly, the virus circulated more frequently in April, the month of peak activity of respiratory HRSV. In 2006 HBoV was detected in only 10 NPAs out of 334 samples (3%) tested, without any notable peak of frequency. In 2007 HBoV was detected in 13 out of 552 (2%) tested samples with little higher frequency of detection in June an July. Rhinorrhea, cough, and wheezing were observed in more than 50% of the HBoV-positive children, and no obvious respiratory clinical differences were noted between HBoV-positive and negative children. However, was noted a higher frequency of diarrhea on HBoV-positive patients. In this study was also observed a larger frequency (71%) of viral coinfections between the HBoV-positive patients. The respiratory viruses more frequently associated with human bocavirus were: HRSV, HRV and HAdV. Interestingly, on the 15 HBoV-alone patients was observed a higher viral load and a higher prevalence of diarrhea than HBoV-coinfection patients. These results showed that this virus can reach enormous titles (like 1014) in NPAs from patients with respiratory infection symptoms and this is associated with diahhrea. The entire genome sequencing of HBoV of our study indicates that the genetic divergence between the HBoV lineages is small. In conclusion, we demonstrated that HBoV circulates and is detected in association with respiratory symptoms and diarrhea in Brazil. Long term surveillance will be needed to determine whether or not an HBoV season occurs and what is the real clinical impact of this virus in our country.

Dans le chapitre 1, nous développons le “corps d’Okounkov” pour une (1,1)-classe pseudo-effective sur une variété kählerienne compacte. Nous démontrons la formule de différentiabilité des volumes de classes grosses pour les varétés kähleriennes sur lesquelles les cônes nef modifiés et les cônes nef coı̈ncident. Par conséquent, nous démontrons l’inégalité de Morse transcendante de Demailly pour ces variétés kähleriennes particulières, y compris les surfaces kähleriennes. Ensuite, nous construisons le corps d’Okounkov généralisé pour toute (1,1)-classe grosse, et nous donnons une caractérisation complète des corps d’Okounkov généralisés sur les surfaces. Nous démontrons que cela se rapporte le volume euclidien standard du corps au volume de la classe grosse correspondant défini par Boucksom, ce qui permet de résoudre un problème proposé par Lazarsfeld et Mustaţă dans le cas des surfaces. Nous étudions aussi le comportement des corps d’Okounkov généralisé sur le bord du cône gros.Dans le chapitre 2, nous étudions la dégénérescence des courbes entières qui sont les feuilles de feuilletages sur des variétés projectives. Nous généralisons l’approximation diophantienne de McQuillan pour les feuilletages de dimension 1 avec des singularités absolument isolées. Comme une application, nous donnons une nouvelle preuve du théorème de Brunella, c’est-à-dire, toutes les feuilles d’un feuilletage générique de degré superieur à 2 dans CP^n est hyperbolique. Ensuite, nous introduisons la notion singularités faiblement réduites pour les feuilletages de dimension 1. L’hypothèse de singularités faiblement réduites est moins exigeante que celle de singularités réduites, mais joue le même rôle dans l’étude de la conjecture de Green-Griffiths-Lang. Finalement, nous discutons d’une stratégie pour démontrer cette conjecture pour les surfaces complexes.Dans le chapitre 3, nous démontrons la non-dégénérescence de la mesure de volume au sens de Kobayashi-Eisenman pour une variété dirigée singulière, c’est-à-dire l’hyperbolicité de la mesure au sens de Kobayashi, lorsque le faisceau canonique est gros au sens de Demailly.Dans le chapitre 4, notre premier objectif est de traiter des questions d’effitivité liées aux conjectures de Kobayashi et Debarre, reliant sur le travail de Brotbek et celui en collaboration avec Darondeau. Ensuite, nous combinons ces techniques pour étudier la conjecture sur l’amplitude des fibrés de Demailly-Semple proposés par Diverio et Trapani, et nous obtenons des estimations effectives liées à ce problème. Notre résultat contient à la fois les conjectures de Kobayashi et Debarre, avec certaines estimations effectives.Le but du chapitre 5 est double: d’une part, nous étudions une conjecture du type Fujita proposée par Popa et Schnell, et nous donnons une borne effective linéaire sur la génération globale générique de l’image directe du faisceau pluricanonique tordu. Nous signalons également la relation entre la constante de Seshadri et la borne optimale. D’autre part, nous donnons une réponse affirmative à une question de Demailly-Peternell-Schneider dans un cadre plus général. Comme des applications, nous généralisons les théorèmes de Fujino et Gongyo sur les images des variétés de Fano faibles aux cas KLT, et nous raffinons un résultat de Broustet et Pacienza sur la connexité rationnelle de l’image.Dans le chapitre 6, nous donnons une preuve concrète et constructive de l’équivalence entre la catégorie de fibrés de Higgs semistables de classes de Chern nulles, et celle des représentations linéaires du groupe fondamental d’une variété kählerienne compacte lisse. / In Part 1 of this thesis, we construct “Okounkov bodies” for an arbitrary pseudo-effective (1,1-class on a Kähler manifold. We prove the differentiability formula of volumes of big classes for Kähler manifolds on which modified nef cones and nef cones coincide. As a consequence we prove Demailly’s transcendental Morse inequality for these particular Kähler manifolds; this includes Kähler surfaces. Then we construct the generalized Okounkov body for any big (1,1)-class, and give a complete characterization of generalized Okounkov bodies on surfaces. We show that this relates the standard Euclidean volume of the body to the volume of the corresponding big class as defined by Boucksom; this solves a problem raised by Lazarsfeld and Mustaţă in the case of surfaces. We also study the behavior of the generalized Okounkov bodies on theboundary of the big cone.Part 2 deals with Kobayashi hyperbolicity-related problems. Chapter 2’s goal is to study the degeneracy of leaves of the one-dimensional foliations on higher dimensional manifolds. The first part of Chapter 2 generalizes McQuillan’s Diophantine approximations for one-dimensional foliations with absolutely isolated singularities, on higher dimensional manifolds. As an application, we give a new proof of Brunella’s hyperbolicity theorem, that is, all the leaves of a generic foliation of degree larger than 2 in CP 6n is hyperbolic. In the second part of Chapter 2 we introduce the so-called weakly reduced singularities for one-dimensional foliations on higher dimensional manifolds. The “weakly reduced singularities” assumption is less demanding than the one required for “reduced singularities”, but play the same role in studying the Green-Griffiths-Lang conjecture. Finally we discuss a strategy to prove the Green-Griffiths-Lang conjecture for complex surfaces.In Chapter 3, assuming that the canonical sheaf is big in the sense of Demailly, we prove theKobayashi volume-hyperbolicity for any (possibly singular) directed variety.In Chapter 4, our first goal is to deal with effective questions related to the Kobayashi and Debarre conjectures, relying on the work of Brotbek and his joint work with Darondeau. We then combine these techniques to study the conjecture on the ampleness of the Demailly-Semple bundles raised by Diverio and Trapani, and also obtain some effective estimates related to this problem. Our result integrates both the Kobayashi and Debarre conjectures, with some effective estimates.The purpose of Chapter 5 is twofold: on the one hand we study a Fujita-type conjecture by Popa and Schnell, and give an effective (linear) bound on the generic global generation of the direct image of the twisted pluricanonical bundle. We also point out the relation between the Seshadri constant and the optimal bound. On the other hand, we give an affirmative answer to a question by Demailly-Peternell-Schneider in a more general setting. As applications, we generalize the theorems by Fujino and Gongyo on images of weak Fano manifolds to the Kawamata log terminal cases, and refine a result by Broustet and Pacienza on the rational connectedness of the image.In Chapter 6, we give a concrete and constructive proof of the equivalence between the category of semistable Higgs bundles with vanishing Chern classes and the category of all representations of the fundamental groups on smooth Kähler manifolds. This chapter is written for the complex geometers who are not familiar with the language of differential graded category used by Simpson to prove the above equivalence on smooth projective manifolds, and for those who would like to see an elementary proof of Corlette-Simpson correspondence for semistable Higgs bundles.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-09T17:52:47Z No. of bitstreams: 1 CARLOS ANTONIO PEREIRA DA SILVA - DISSERTAÇÃO PPGMAT 2014..pdf: 597533 bytes, checksum: 741e2e32988fe89dd00df90b6aa0c5c9 (MD5) / Made available in DSpace on 2018-08-09T17:52:47Z (GMT). No. of bitstreams: 1 CARLOS ANTONIO PEREIRA DA SILVA - DISSERTAÇÃO PPGMAT 2014..pdf: 597533 bytes, checksum: 741e2e32988fe89dd00df90b6aa0c5c9 (MD5) Previous issue date: 2014-08 / Capes / Neste trabalho, como uma aplicação adequada do bem conhecido Princípio do Máximo Generalizado de Omori-Yau, obtemos resultados relativos a rigidez para hipersuperfícies tipo-espaço completas imersas na metade Hn+1 do espaço de De Sitter Sn+11 , que é chamado de steady state space. Por outro lado, usando uma isometria equivalente para o modeloHn+1, estenderemos nossos resultados a uma família maior de espaços-tempos. Por fim, estudaremos também a singularidade de gráficos verticais inteiros nesses espaços-tempos ambiente. / In this work, as a suitable application of the well known generalized Maximum Principle of Omori-Yau, we obtain rigidity results concerning to complete spacelike hypersurfaces immersed in the half Hn+1 of the de Sitter spaceSn+11 , which models the so-called steady state space. Moreover, by using an isometrically equivalent model for Hn+1, we extend our results to a wider family of spacetimes. Finally, we also study the uniqueness of entire vertical graphs in such ambient spacetimes.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-07-25T19:25:58Z No. of bitstreams: 1 ERALDO ALMEIDA LIMA JÚNIOR - DISSERTAÇÃO PPGMAT 2011..pdf: 415901 bytes, checksum: 427abfdae7c5a546735d4a6b14f72bfe (MD5) / Made available in DSpace on 2018-07-25T19:25:58Z (GMT). No. of bitstreams: 1 ERALDO ALMEIDA LIMA JÚNIOR - DISSERTAÇÃO PPGMAT 2011..pdf: 415901 bytes, checksum: 427abfdae7c5a546735d4a6b14f72bfe (MD5) Previous issue date: 2011-07 / Neste trabalho, apresentamos um estudo das hipersuperfícies tipo-espaço imersas no ambiente −R × Hn, exibindo condições para que tais hipersuperfícies sejam slices {t0}×Hn. Para uma melhor compreensão das demonstrações e dos resultados, inserimos processos de diferenciação, cálculos de gradientes e Laplacianos que, juntamente com o princípio do máximo de Omori-Yau, foram cruciais no desenvolvimento dos resultados que, em sua maioria são do tipo Bernstein. Também incluímos um resultado do tipo Calabi. / In this work we present a study of the spacelike hypersurfaces immersed in the manifold −R × Hn providing sufficient conditions for such hypersurfaces be slices, {t0}×Hn. For a better understanding of the proofs and results, we have added differentiation processes, gradient computations and Laplacians which jointly with the Omori-Yau Maximum Principle were crucial in the developing of the results whose are mostly Bernstein-type. In the elapsing we also included Calabi-type results.