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

Poon Chi Cheung. / Bibliography: leaves 66-69 / Thesis (M.Ph.)--Chinese University of Hong Kong, 1986

by Leung Kwok Kei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 90-94). / Chapter 0 --- Introduction --- p.1 / Chapter 1 --- Comparison Theorems --- p.4 / Chapter 1.1 --- Introduction --- p.4 / Chapter 1.2 --- Bishop Comparison Theorem --- p.5 / Chapter 1.3 --- Hessian Comparison Theorem --- p.13 / Chapter 1.4 --- Applications of Laplacian comparison theorem --- p.16 / Chapter 2 --- "The first eigenvalue, gradient estimates and related inequalities" --- p.21 / Chapter 2.1 --- Lower bounds of the first eigenvalue --- p.21 / Chapter 2.2 --- Gradient estimate and Harnack inequality --- p.29 / Chapter 2.3 --- Mean value inequality --- p.33 / Chapter 2.4 --- Isoperimetric inequalities and Sobolev inequalities --- p.40 / Chapter 3 --- Harmonic mappings --- p.47 / Chapter 3.1 --- Definitions and notations --- p.47 / Chapter 3.2 --- Existence results --- p.50 / Chapter 3.3 --- Bochner technique --- p.54 / Chapter 3.4 --- Strong rigidity theorems --- p.58 / Chapter 3.5 --- Superrigidity and harmonic maps --- p.71 / Appendix --- p.75 / Chapter A --- Bochner formula and its integral form --- p.76 / Chapter A.1 --- Bochner formula --- p.76 / Chapter A.2 --- Reilly's formula and its applications --- p.82 / Bibliography --- p.90

by Cheung Wing Sum. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1980. / Bibliography: leaves 94-98.

by Lung Tak Yee. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaves 80-82.

by Wu Man Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 60-62). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Harmonic functions with linear growth --- p.3 / Chapter 2.1 --- A sharp estimate for dim H1 (M) --- p.3 / Chapter 2.2 --- Linear growth harmonic functions on Kahler manifolds --- p.8 / Chapter 3 --- Harmonic functions of polynomial growth --- p.21 / Chapter 3.1 --- Harmonic sections of polynomial growth --- p.21 / Chapter 3.2 --- Harmonic functions on manifolds with Sobolev in- equality --- p.34 / Chapter 4 --- Harmonic functions on manifolds with nonnegat --- p.ive / sectional curvature --- p.43 / Bibliography --- p.60

Cheng Man Chuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 78-80). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Different Notions of Negative Curvatures for Kahler Manifolds --- p.3 / Chapter 2.1 --- Definitions --- p.3 / Chapter 2.2 --- Adequate negativity of curvatures of classical domains of type I --- p.13 / Chapter 2.3 --- Adequate negativity of curvatures of classical domains of type IV --- p.23 / Chapter 2.4 --- Structure of complex semi-simple Lie algebra and its relation with Hermitian symmetric spaces --- p.28 / Chapter 2.5 --- Adequate negativity of curvatures of classical domains of type II and III --- p.34 / Chapter 2.6 --- Adequate negativity of curvatures of the two excep- tional bounded symmetric domains --- p.45 / Chapter 3 --- Complex-analyticity of Harmonic Maps between Compact Kahler Manifolds --- p.50 / Chapter 3.1 --- Existence of harmonic maps --- p.50 / Chapter 3.2 --- A Bochner type identity --- p.51 / Chapter 3.3 --- Complex-analyticity of harmonic maps --- p.58 / Chapter 3.4 --- Strong rigidity theorems --- p.62 / Chapter 3.5 --- Some further results from the Bochner technique --- p.64 / Chapter 4 --- Generalization to the Non-compact case --- p.67 / Chapter 4.1 --- A strong rigidity theorem for non-compact Kahler manifolds --- p.67 / Chapter 4.2 --- An existence theorem of harmonic map for Rieman- nian manifolds of finite volumes --- p.69 / Chapter 4.3 --- Bochner formula in the non-compact case --- p.71 / Bibliography --- p.78

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

Chan Kwok Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 78-81). / Abstracts in English and Chinese. / Chapter 1 --- Introduction to Toric Geometry --- p.7 / Chapter 1.1 --- Definitions of Toric Varieties --- p.7 / Chapter 1.2 --- Properties of Toric Varieties --- p.11 / Chapter 1.2.1 --- Smoothness --- p.12 / Chapter 1.2.2 --- Compactness --- p.12 / Chapter 1.2.3 --- Stratification --- p.13 / Chapter 1.3 --- Divisors on Toric Varieties --- p.14 / Chapter 1.3.1 --- Weil divisors --- p.14 / Chapter 1.3.2 --- Cartier divisors --- p.14 / Chapter 1.4 --- Polarized Toric Varieties --- p.16 / Chapter 2 --- Calabi-Yau Manifolds from Toric Varieties --- p.19 / Chapter 2.1 --- Toric Fano Varieties --- p.19 / Chapter 2.2 --- Calabi-Yau Hypersurf aces in Toric Fano Varieties --- p.23 / Chapter 2.3 --- Computation of Hodge Numbers of Zf --- p.28 / Chapter 2.3.1 --- The results of Danilov and Khovanskii --- p.29 / Chapter 2.3.2 --- "The Hodge number hn-2,1(Zf)" --- p.31 / Chapter 2.3.3 --- "The Hodge number hl,1(zf)" --- p.32 / Chapter 2.4 --- Calabi-Yau Complete Intersections in Toric Fano Va- rieties --- p.34 / Chapter 3 --- Calabi-Yau Manifolds by Quotients --- p.41 / Chapter 3.1 --- Free Group Actions --- p.41 / Chapter 3.2 --- Crepant Resolutions of Orbifolds --- p.44 / Chapter 3.3 --- Examples From Complex Tori --- p.49 / Chapter 3.4 --- Complex Multiplication and Calabi-Yau Threefolds --- p.51 / Chapter 4 --- Calabi-Yau Manifolds by Coverings --- p.56 / Chapter 4.1 --- Cyclic Coverings --- p.56 / Chapter 4.2 --- Admissible Blow-ups --- p.57 / Chapter 4.3 --- Double Covers of P3 Branched Along Octic Arrang- ments --- p.59 / Chapter 4.4 --- The Euler Number of X --- p.61 / Chapter 4.5 --- The Hodge Numbers of X --- p.65 / Chapter 4.6 --- K3-Fibrations and Modularity --- p.69 / Chapter 0 --- Bibliography --- p.78

Mak, Kin Hei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 48-50). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.2 / Chapter 2 --- Symplectic 4-Manifolds --- p.5 / Chapter 2.1 --- Basic Definitions --- p.5 / Chapter 2.2 --- Simple Examples of Symplectic Manifolds --- p.6 / Chapter 2.3 --- A Theorem of Thurston --- p.8 / Chapter 2.4 --- Lefschetz Pencils --- p.13 / Chapter 3 --- Classification of Lefschetz Fibrations --- p.17 / Chapter 3.1 --- Definitions --- p.17 / Chapter 3.2 --- Handlebody Decomposition --- p.19 / Chapter 3.3 --- Genus 1 --- p.29 / Chapter 3.4 --- Genus 2 --- p.36 / Chapter 3.5 --- Genus g≥3 --- p.43 / Bibliography --- p.48