No description available.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references and index.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 44)

In this thesis we prove the existence of vector-valued automorphic forms for an arbitrary Fuchsian group and an arbitrary finite dimensional complex representation of this group. For small enough values of the weight as well as for large enough values, we provide explicit formulas for the spaces of these vector-valued automorphic forms (holomorphic and cuspidal). To achieve these results, we realize vector-valued automorphic forms as global sections of a certain family of holomorphic vector bundles on a certain Riemann surface associated to the Fuchsian group. The dimension formulas are then provided by the Riemann-Roch theorem. In the cases of 1 and 2-dimensional representations, we give some applications to the theories of generalized automorphic forms and equivariant functions.

No description available.

Thesis (Dr. rer. nat.)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2002. / Includes bibliographical references (p. 49-50).

A generalization of a theorem of N.R. 0'Brian, zeroes of holomorphic vector fields and the Grothendieck residue, Bull. London Math. Soc, 7 (1975) is given. The theorem of Riemann-Roch and Hirzebruch for V-equivariant holomorphic vector bundles is obtained, via holomorphic vector fields, in the case all zeroes of the holomorphic vector field V are isolated. The Bruhat decomposition of G/B is obtained from the G -action on G/B . It is shown that a theorem of A. Bialynicki-Birula, Some theorems on actions of algebraic groups, Ann. of Math. 98, 480-497 (1973) is the generalization of the Bruhat decomposition on G/B , which was a conjecture of B. Iversen. The existence of a G -action on G/P with only one fixed a point is proved, where G is a connected linear algebraic group defined over an algebraically closed field k of characteristic zero and P is a parabolic subgroup of G . The following is obtained P = N[sub G](Pu) = {geG: Adg(Pu) = Pu} where G is a connected linear algebraic group, P is a parabolic subgroup of G and P^ is the tangent space of the set of unipotent elements of P at the identity. An elementary proof of P = N[sub G](P) = {geG: gPg ⁻¹=P} is given, where G is a connected linear algebraic group and P is a parabolic subgroup of G . / Science, Faculty of / Mathematics, Department of / Graduate

by Leung Wai-Man Raymond. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves [1]-[3] (2nd gp.)). / Chapter CHAPTER 0 --- Introduction --- p.1 / Chapter CHAPTER 1 --- Einstein-Hermitian Vector Bundles / Chapter 1.1 --- Preliminaries on Einstein-Hermitian structures --- p.4 / Chapter 1.2 --- Conformal invariance --- p.7 / Chapter 1.3 --- A Chern number inequality --- p.9 / Chapter CHAPTER 2 --- Stable Vector Bundles / Chapter 2.1 --- Coherent analytic sheaves --- p.12 / Chapter 2.2 --- "Torsion-free, reflexive and normal coherent analytic sheaves" --- p.18 / Chapter 2.3 --- Determinant bundles --- p.22 / Chapter 2.4 --- Stable vector bundles --- p.27 / Chapter 2.5 --- Stability of Einstein-Hermitian vector bundles --- p.32 / Chapter CHAPTER 3 --- Existence of Einstein-Hermitian connection on stable vector bundle over a compact Riemann Surface --- p.34 / Chapter CHAPTER 4 --- Existence of Einstein-Hermitian metric on stable vector bundle over a projective algebraic manifold / Chapter 4.1 --- Solution of the evolution equation for finite time --- p.45 / Chapter 4.2 --- Convergence of solution for infinite time --- p.53 / APPENDIX / Chapter I. --- A vanishing theorem of Bochner type and its consequences --- p.67 / Chapter II. --- Uhlenbeck's results on connections with Lp bounds on curvature --- p.69 / REFERENCE

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 20-21). Also available in electronic version. Access restricted to campus users.

Thesis (doctoral)--Universität Bonn, 1988. / Cover title: Integraldarstellungen und a priori-Abschätzungen für das [delta bar]-Neumann-Problem. Includes bibliographical references (p. 94-96).