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Deformation theory of compact complex manifolds and CR manifolds.

Ng Wai Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 87-88). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Infinitesimal Deformations for Compact Complex Manifolds --- p.4 / Chapter 2.1 --- Differentiable Family --- p.4 / Chapter 2.2 --- Local Triviality --- p.7 / Chapter 2.3 --- Complex Analytic Family and Deformations --- p.10 / Chapter 3 --- Existence Theorem --- p.15 / Chapter 3.1 --- Obstructions as a Necessary Condition --- p.15 / Chapter 3.2 --- The Existence Theorem --- p.16 / Chapter 3.3 --- Convergence Proof --- p.21 / Chapter 4 --- Completeness Theorem --- p.26 / Chapter 4.1 --- The Completeness Theorem --- p.26 / Chapter 4.2 --- Construction of Formal Power Series --- p.28 / Chapter 4.3 --- Convergence Proof --- p.32 / Chapter 4.4 --- Effective Parameters and Number of Moduli --- p.36 / Chapter 4.5 --- Examples --- p.40 / Chapter 5 --- CR Manifolds and Deformations --- p.42 / Chapter 5.1 --- CR Submanifolds and Tangential Complex --- p.42 / Chapter 5.2 --- Abstract CR Manifolds and its Cohomologies --- p.47 / Chapter 5.3 --- Strongly Pseudoconvex Manifolds --- p.51 / Chapter 5.4 --- Differentiable Family --- p.53 / Chapter 6 --- Stability Theorems --- p.55 / Chapter 6.1 --- Semi-continuity Theorem --- p.56 / Chapter 6.1.1 --- The Case of Compact Complex Manifolds --- p.56 / Chapter 6.1.2 --- The s.p.c. Compact CR Case --- p.63 / Chapter 6.2 --- Other Stability Theorems for Complex Manifolds --- p.66 / Chapter A --- The Complex Laplacian ´بa --- p.72 / Chapter B --- Hodge-Dolbeault Theorem --- p.77 / Chapter C --- Proof of Theorem 6.2 --- p.79 / Chapter D --- Subelliptic Estimates of --- p.82 / Bibliography --- p.87

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_325811
Date January 2006
ContributorsNg, Wai Man., Chinese University of Hong Kong Graduate School. Division of Mathematics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, v, 88 leaves ; 30 cm.
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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