Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-13T11:21:20Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Cid Dias Ferraz Machado - 2014.pdf: 1785087 bytes, checksum: 2f0dd6f0844c3aa992b9eaf248f40ed4 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-13T11:22:09Z (GMT) No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Cid Dias Ferraz Machado - 2014.pdf: 1785087 bytes, checksum: 2f0dd6f0844c3aa992b9eaf248f40ed4 (MD5) / Made available in DSpace on 2015-01-13T11:22:10Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Cid Dias Ferraz Machado - 2014.pdf: 1785087 bytes, checksum: 2f0dd6f0844c3aa992b9eaf248f40ed4 (MD5) Previous issue date: 2014-03-07 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this work we present a study of a class of oriented hypersurfaces in hyperbolic space satisfying a special linear relation between the rth mean curvatures which is based on a Walterson Ferreira and Pedro Roitman’s article, where this class is characterized by a harmonic map derived from the two hyperbolic Gauss maps.We also show the relation of such hypersufaces with solutions of the equation Du+kun+2 n􀀀2 = 0, where k 2 f􀀀1;0;1g. / Neste trabalho apresentamos um estudo de uma classe de hipersuperfícies orientadas no espaço hiperbólico satisfazendo uma relação linear especial entre as r-ésimas curvaturas médias, baseado no trabalho de Walterson Ferreira e Pedro Roitman, onde esta classe é caracterizada por uma aplicação harmônica derivada das duas aplicações hiperbólicas de Gauss. Também mostramos a relação de tais hipersuperfícies com as soluções da equação Du+kun+2 n􀀀2 = 0, onde k 2 f􀀀1;0;1g.

Made available in DSpace on 2014-07-29T16:02:17Z (GMT). No. of bitstreams: 1 Dissertacao Fang pdf.pdf: 960409 bytes, checksum: c8b4323e6ccb3bedc18f73796fe0f97c (MD5) Previous issue date: 2011-03-25 / The main objective is to study the curves generated by the front and rear wheels of a bicycle from the standpoint of differential geometry. / O principal objetivo deste trabalho é estudar as curvas geradas pelas rodas traseira e dianteira de uma bicicleta do ponto de vista da Geometria diferencial.

Submitted by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2018-05-22T14:42:33Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) h-Quase Sóliton de Ricci.pdf: 40561599 bytes, checksum: 88a9a69eec01fab6046ed43b9b7d63b9 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2018-05-22T14:42:51Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) h-Quase Sóliton de Ricci.pdf: 40561599 bytes, checksum: 88a9a69eec01fab6046ed43b9b7d63b9 (MD5) / Made available in DSpace on 2018-05-22T14:42:51Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) h-Quase Sóliton de Ricci.pdf: 40561599 bytes, checksum: 88a9a69eec01fab6046ed43b9b7d63b9 (MD5) Previous issue date: 2016-12-01 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work we study the concept h-almost Ricci soliton introduced by Gomes-Wang-Xia which extends naturally the almost Ricci soliton studied by Pigola et al. In this setting, we show that a compact nontrivial h-almost Ricci soliton of dimension no less than three with h positive (or negative) and constant scalar curvature is isometric to a standard sphere with well defined potential function. Latter on, we also consider h-Ricci soliton which is a particular case of the h-almost Ricci soliton and a generalization of the traditional Ricci soliton. We prove that a particular case of compact gra-dient h-Ricci soliton steady or expanding, is trivial. Moreover, we give a characterization for a special class of gradient h-Ricci solitons. / Neste trabalho vamos estudar o conceito de h-quase sólitons de Ricci introduzido por Gomes-Wang-Xia o qual é uma extensão natural dos quase sólitons de Ricci estudados por Pigola et al. Com esta configuração, vamos mostrar que um h-quase sóliton de Ricci compacto de curvatura escalar constante não-trivial de dimensão maior ou igual a três e li possuindo sinal definido é isométrico a uma esfera euclidiana com função potencial explicita-mente definida. Logo após, também vamos considerar h-sólitons de Ricci os quais são casos particulares dos h-quase sólitons de Ricci e uma generalização dos tradicionais sólitons de Ricci. Vamos provar que um caso particular de h-sóliton de Ricci gradiente compacto estacionário ou expansivo, é trivial. Além disso, exibiremos uma caracterização para uma classe especial de h-sólitons de Ricci gradiente.

Submitted by Franciele Moreira (francielemoreyra@gmail.com) on 2017-12-27T13:50:44Z No. of bitstreams: 2 Tese - Wesley da Silva Ruys - 2017.pdf: 2660976 bytes, checksum: 3c6402ac0974e65da560b50e1f65b52e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-12-28T09:42:07Z (GMT) No. of bitstreams: 2 Tese - Wesley da Silva Ruys - 2017.pdf: 2660976 bytes, checksum: 3c6402ac0974e65da560b50e1f65b52e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-12-28T09:42:07Z (GMT). No. of bitstreams: 2 Tese - Wesley da Silva Ruys - 2017.pdf: 2660976 bytes, checksum: 3c6402ac0974e65da560b50e1f65b52e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-12-07 / Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG / In this work we present a classification of the Laguerre minimal surfaces with flat curvature lines. We introduce three classes of hypersurfaces that generalize the Laguerre minimal surfaces with the prescribed Gaussian normal application. The first class is associated to biharmonic applications and is related by a Legendre transformation to hypersurfaces that in the isotropic model has harmonic isotropic mean curvature. As an application, we classify the hypersurfaces of rotation and we present examples of these hypersurfaces parameterized by flat curvature lines. We obtain a characterization of the other two classes of hypersurfaces, we study the rotation ones and we present examples. / Neste trabalho apresentamos uma classificação das superfícies mínimas de Laguerre com linhas de curvatura planas. Introduzimos três classes de hipersuperfícies que generalizam as superfícies mínimas de Laguerre com aplicação normal de Gauss prescrita. A primeira classe está associada a aplicações biharmônicas e está relacionada por uma transformação de Legendre a hipersuperfícies que no modelo isotrópico tem curvatura média isotrópica harmônica. Como aplicação, classificamos as hipersuperfícies de rotação e apresentamos exemplos destas hipersuperfícies parametrizadas por linhas de curvatura planas. Obtemos uma caracterização das outras duas classes de hipersuperfícies, estudamos as de rotação e apresentamos exemplos.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2017-04-24T22:03:45Z No. of bitstreams: 2 Dissertação - Hector Andrés Rosero García - 2017.pdf: 4670148 bytes, checksum: 8bc0d1f8d189cce09af8bc129ec5edcd (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-04-25T15:46:02Z (GMT) No. of bitstreams: 2 Dissertação - Hector Andrés Rosero García - 2017.pdf: 4670148 bytes, checksum: 8bc0d1f8d189cce09af8bc129ec5edcd (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-04-25T15:46:02Z (GMT). No. of bitstreams: 2 Dissertação - Hector Andrés Rosero García - 2017.pdf: 4670148 bytes, checksum: 8bc0d1f8d189cce09af8bc129ec5edcd (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-03-31 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this work we develop the basics of the concept of Isocurved Surface, introduced in [2] by Barroso and Roitman, that is, a surface immersed in a 3-dimensional manifold M and which have the same Gaussian curvature induced by two different metrics. Later on, we show a geometric method to generate non-trivial examples of elliptic and hyperbolic isocurved surfaces for the particular case of M = R3+ and the Euclidean and hyperbolic metrics induced on it. We also exhibit some examples coming from the geometric method above. / Neste trabalho, desenvolvemos as bases do conceito de Superfície Isocurvada, introduzido em [2] por Barroso e Roitman, isto é, uma superfície imersa numa variedade 3-dimensional M a qual tem a mesma curvatura Gaussiana induzida por duas métricas diferentes em M. Segundo isso, mostramos um método geométrico para a geração de exemplos não triviais de superfícies isocurvadas elípticas e hiperbólicas no caso particular de M = R^3_+ com as métricas conformes Euclidiana e hiperbólica. Também exibimos alguns exemplos subjacentes ao método acima.

This thesis explores and explains a method using discrete curvature as a feature to find regions of vertices that can be classified as being likely to indicate the presence of an underlying tumor on a kidney surface mesh. Vertices are tagged based on curvature type and mathematical morphology is used to form regions on the mesh. The size and location of the tumor is approximated by fitting a sphere to this region. The method is intended to be employed in noninvasive radiotherapy with a dynamic soft tissue model. It could also provide an alternative to volumetric methods used to segment tumors. A validation is made using the images from which the kidney mesh was constructed, the tumor is visible as a comparison to the method result. The dynamic kidney model is validated using the Hausdorff distance and it is explained how this can be computed in an effective way using bounding volume hierarchies. Both the tumor finding method and the dynamic model show promising results since they lie within the limit used by practitioners during therapy.

Le problème de la limite continue de la gravitation quantique à boucle est encore ouvert. En effet, la dynamique précise n’est pas connue et nous ne disposons pas des outils nécessaires à l’étude de cette limite le cas échéant. Dans cette thèse, nous étudions quelques méthodes de coarse-graining (étude à gros grains) qui devraient contribuer à cette entreprise. Nous nous concentrons sur deux aspects du flot: la détermination d’observables naturelles à grandes échelles d’un côté et la manière de s’abstraire du problème de la dynamique à graphe variable en la projetant sur des graphes fixes de l'autre.Pour déterminer les observables aux grandes distances, nous étudions le cas des tétraèdres hyperboliques et leur description naturelle dans un langage proche de celui de la gravitation quantique à boucle. Les holonomies de surface en particulier jouent un rôle important. Cela dégage la structure des double spin networks constitués d'un graphe et de son dual, structure qui semble aussi apparaître dans les travaux de Freidel et al. Pour résoudre le problème des graphes variables, nous considérons et définissons les loopy spin networks. Ils encodent par des boucles la courbure locale d'un vertex effectif et permettent ainsi de décrire différents graphes en les masquant via le processus de coarse-graining. De plus, leur définition donne un procédé naturel systématique de coarse-graining pour passer d'une échelle à une autre.Ensemble, ces deux principaux résultats posent le fondement d'un programme de coarse-graining pour les théories invariantes sous difféomorphismes. / The continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-be continuum limit. In the present PhD dissertation, we will investigate some coarse-graining methods that should become helpful in this enterprise. We concentrate on two aspects of the theory's coarse-graining: finding natural large scale observables on one hand and studying how the dynamics of varying graphs could be cast onto fixed graphs on the other hand.To determine large scale observables, we study the case of hyperbolic tetrahedra and their natural description in a language close to loop quantum gravity. The surface holonomies in particular play an important role. This highlights the structure of double spin networks, which consist in a graph and its dual, which seems to also appear in works from Freidel et al. To solve the problem of varying graphs, we consider and define loopy spin networks. They encode the local curvature with loops around an effective vertex and allow to describe different graphs by hidding them in a coarse-graining process. Moreover, their definition gives a natural procedure for coarse-graining allowing to relate different scales.Together, these two results constitute the foundation of a coarse-graining programme for diffeomorphism invariant theories.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / We study problems of existence and uniqueness of constant mean curvature surfaces with prescribed boundary satisfying the bounded slope condition. The surfaces are given as Euclidean graphs in R3 and as parabolic graphs in H3, over bounded domains contained in totally geodesic surfaces in these ambients, or moreover, as radial graphs over bounded domains contained in S2. / Estudamos problemas de existência e unicidade de superfícies de curvatura média constante com bordo prescrito satisfazendo a condição de declividade limitada (CDL). Tais superfícies são dadas como gráficos euclidianos (verticais) em R3 e como gráficos parabólicos em H3, definidos sobre domínios limitados contidos em superfícies totalmente geodésicas destes ambientes, ou ainda como gráficos radiais em R3 sobre domínios limitados contidos em S2.

Dans cette thèse, nous nous intéressons aux espaces temps dit globalement hyperboliques Cauchy compacts. Ce sont des espaces temps qui admettent une fonction, dite fonction temps de Cauchy, propre qui croit strictement le long des courbes causales inextensibles. Les niveaux de telles fonctions sont des hypersurfaces de type espace appelées hypersurfaces de Cauchy. La donnée d'une fonction temps définit naturellement une famille à 1-paramètres d'espaces métriques. Notre but est d'étudier le comportement asymptomatique de ces familles d'espaces métriques Il y a deux cas de figure à considérer : le premier étant le comportement asymptomatique dans le passé ; le deuxième est celui du comportement asymptomatique dans le futur. Plus de conditions géométriques sur l'espace temps et les fonctions temps à considérer seront nécessaires / In this thesis we're interested in globally hyperbolic Cauchy compact space-times. These are space-times that possess a proper function, called Cauchy time function, which ist strictly increasing along inextensible causal curves. A Cauchy time function defines naturally a 1-parameter family of metric spaces. One asks the natural and important question of the asymptomatic behaviour of this family with respect to the time : when time goes to 0 and when it goes towards infinity. Of course additional geometric condition on the space-ime and the time function will be necessary for a more appropriate study

Ce travail de thèse porte sur la modélisation dynamique 3D du rein et le suivi d’une tumeur de cet organe. Il s’inscrit dans le projet KiTT (Kidney Tumor Tracking) qui regroupe des chercheurs issus de plusieurs domaines : la modélisation géométrique, la radiologie et l’urologie. Le cadre de cette thèse suit une tendance de mini-invasivité des gestes chirurgicaux observée ces dernières années (HIFU, coelioscopie). Sa finalité est d’aboutir à un nouveau protocole de destruction de tumeurs rénales totalement non-invasif, par la diffusion d’agents physiques (ondes d’ultrasons) à travers la peau et focalisés sur la tumeur. Devant le mouvement et la déformation que le rein présente au cours du cycle respiratoire, la problématique de ces travaux de recherche est de connaître en permanence la position de la tumeur afin d’ajuster à moyen terme la diffusion des ondes en conséquence. / This Ph.D. thesis deals with the 3D dynamic modeling of the kidney and tracking a tumor of this organ. It is in line with the KiTT project (Kidney Tumor Tracking) which gathers researchers from different fileds: geometric modeling, radiology and urology. This work arised from the tendency of nowadays surgical gestures to be less and less invasive (HIFU, coelioscopy). Its goal is to result in a totally non-invasive protocol of kidney tumors eradication by transmitting ultrasound waves through the skin without breaking in it. As the kidney presents motions and deformations during the breathing phase, the main issue is to know the kidney and tumor positions at any time in order to adjust the waves accordingly.