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Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

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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.

Ma, Chit. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 61-63). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Sasaki Geometry --- p.8 / Chapter 2.1 --- Sasakian manifolds --- p.8 / Chapter 2.2 --- Transversal Kahler geometry --- p.11 / Chapter 2.3 --- Sasaki-Futaki invariant --- p.16 / Chapter 2.3.1 --- Space of Kahler cone metric --- p.17 / Chapter 2.3.2 --- Futaki invariant --- p.20 / Chapter 2.3.3 --- A formula for volume variation --- p.27 / Chapter 3 --- Toric Geometry --- p.30 / Chapter 3.1 --- Toric Kahler geometry --- p.30 / Chapter 3.2 --- Toric Sasakian manifold --- p.42 / Chapter 3.3 --- Ricci flat metric in toric Kahler-Sasaki cone --- p.47 / Chapter 4 --- Chern numbers inequality --- p.55

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.

Thesis (Ph. D.)--Michigan State University. Dept. of Mathematics, 2008. / Title from PDF t.p. (viewed on July 23, 2009) Includes bibliographical references (p. 106-108). Also issued in print.

Thesis (Dr. rer. nat.)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2001. / Includes bibliographical references (p. 87-90).