published_or_final_version / abstract / toc / Mathematics / Master / Master of Philosophy

by Mong Kai Cheong. / Bibliography: leaf 50 / Thesis (M.Phil.)--Chinese University of Hong Kong, 1983

by Chen Bing-Long. / "August 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 68-71). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

published_or_final_version / Mathematics / Master / Master of Philosophy

by Tsang Yau Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 79-83). / Contents --- p.1 / Chapter Chapter 0 --- Introduction --- p.1 / Chapter Chapter 1. --- Elliptic Case --- p.4 / Chapter 1.1 --- Existence of energy minimizing maps --- p.6 / Chapter 1.2 --- Complex analyticity of energy minimizing maps --- p.9 / Chapter 1.3 --- Holomorphic deformation of rational curves --- p.15 / Chapter 1.4 --- End of proof and further remarks --- p.25 / Chapter Chapter 2. --- Parabolic Case --- p.30 / Chapter 2.1 --- Construction of non-vanishing holomorphic n-form --- p.32 / Chapter 2.2 --- Construction of functions of minimal degree --- p.50 / Chapter 2.3 --- Construction of biholomorphism using minimal degree functions --- p.53 / Chapter Chapter 3. --- Hyperbolic Case --- p.59 / Chapter 3.1 --- Various types of negative curvature conditions --- p.61 / Chapter 3.2 --- A Bochner type identity --- p.63 / Chapter 3.3 --- Complex analyticity of harmonic maps --- p.66 / Chapter 3.4 --- Bounded symmetric domains --- p.73 / Chapter 3.5 --- "Strong ""rigidity"" and other applications" --- p.76 / Bibliography --- p.79

Li Changzheng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 43-44). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Preliminaries --- p.3 / Chapter 2.1 --- Clifford Algebras --- p.3 / Chapter 2.2 --- Spin Representation and Spinor Bundles --- p.7 / Chapter 2.3 --- Normed Division Algebras --- p.11 / Chapter 3 --- Associated Representations on /\. V* --- p.15 / Chapter 3.1 --- Exterior Forms and Spinors --- p.15 / Chapter 3.2 --- Direct Calculations --- p.16 / Chapter 3.3 --- "u(l,l,K) Action on V + V*" --- p.24 / Chapter 3.4 --- "su(l,l,K)´so(R1´ة0+K)" --- p.30 / Chapter 4 --- Some Applications to Geometry --- p.35 / Chapter 4.1 --- Holonomy Representations and Spinor Bundles --- p.35 / Chapter 4.2 --- The Lefschetz Action: Kahler Case --- p.37 / Chapter 4.3 --- The Lefschetz Action: HyperKahler Case --- p.41 / Bibliography --- p.43

Yu Chengjie. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 65-67). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgments --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- A multiplicity estimate and applications --- p.5 / Chapter 2.1 --- A multiplicity estimate --- p.6 / Chapter 2.2 --- Sharp bounds for the dimensions of the spaces of holomorphic functions of polynomial growth --- p.14 / Chapter 2.3 --- Siegel's theorem on the fields of rational functions --- p.15 / Chapter 3 --- Quasi-embedding of complete Kahler manifolds --- p.21 / Chapter 3.1 --- The original map F0 --- p.21 / Chapter 3.2 --- Almost injectivity of F0 --- p.26 / Chapter 3.3 --- Almost surjectivity of F0 --- p.28 / Chapter 3.4 --- Weaker conditions for almost surjectivity --- p.41 / Chapter 3.5 --- Existence of quasi-embedding --- p.48 / Chapter 4 --- Desingularization of quasi-embeddings --- p.51 / Chapter 4.1 --- Normalization of a map with polynomial growth --- p.51 / Chapter 4.2 --- The method to desingularize a quasi-embedding --- p.54 / Chapter 4.3 --- The case of dimension two --- p.55 / Chapter 4.4 --- A uniformization theorem --- p.63 / Bibliography --- p.65

In this thesis, we will first extend the pseudo-locality of the Ricci flow on compact Riemannian manifolds discovered by Perelman to complete noncompact Riemannian manifolds. Then, we will apply it to study the long time existence of the Kahler-Ricci flow on complete noncompact Kahler manifolds with reasonable geometric assumptions. Finally, we will give some examples of complete flat Kahler metrics on the complex projective space with some divisor deleted. / by Yu, Chengjie. / Advisers: Yau-Heng Wan; Luen-Fai Tam. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3552. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 113-116). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

by Fan Xuqian. / "August 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 84-87). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Two special classes of solutions to the Yang-Mills equations are studied in this thesis; Hermitian-Einstein connections on holomorphic bundles over Kahler manifolds, and self-dual connections on bundles over Riemannian 4-manifolds. We give a new proof of a theorem of Narasimhan and Seshadri, which characterizes those holomorphic bundles over an algebraic curve admitting projectively flat connections, and describe a conjecture of Hitchin and Kobayashi that would extend this to Hermitian-Einstein connections over any smooth projective variety. This conjecture is proved to be true for the simplest interesting case: bundles of rank 2 over ℙ². Moduli spaces of self-dual connections are studied from the point of view of differential topology, For bundles of Chern class -1 over a simply connected 4-manifold this moduli space can be compactified in a straightforward way and is, in a generic sense, an orientable manifold with quotient singularities. Applying the theory of cobordism to this moduli space we deduce that there are severe constraints on the matrices which can be realised by the intersection pairing on the second homology group of a smooth 4-manifold.