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.

Yau, Sin Wa. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 78-80). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgements --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Morse Theory --- p.3 / Chapter 2.1 --- Definition --- p.3 / Chapter 2.2 --- Existence of Morse functions --- p.4 / Chapter 2.3 --- Properties of Morse functions --- p.7 / Chapter 2.4 --- The Morse homology --- p.16 / Chapter 2.4.1 --- Counting the number of flow lines with sign --- p.18 / Chapter 2.4.2 --- The Morse complex and the Morse homology --- p.19 / Chapter 2.5 --- The Morse inequality --- p.27 / Chapter 3 --- The Novikov homology --- p.29 / Chapter 3.1 --- The Novikov complex --- p.29 / Chapter 3.2 --- Relates the Novikov homology to the singular homology --- p.39 / Chapter 3.3 --- Properties of the Novikov homology --- p.43 / Chapter 3.4 --- The Novikov inequality and some applications --- p.51 / Chapter 4 --- Comparion with classical Morse theory --- p.55 / Chapter 5 --- Applications to knots and links --- p.58 / Chapter 5.1 --- Regular Morse functions --- p.58 / Chapter 5.2 --- The Morse-Novikov number --- p.74 / Chapter 5.3 --- The Universal Novikov homology --- p.76 / Bibliography --- p.78

Wu, Lijiang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 102-105). / Abstracts in English and Chinese. / Chapter 0 --- Introduction --- p.6 / Chapter 1 --- Background knowledge --- p.9 / Chapter 1.1 --- Comparison theorems --- p.9 / Chapter 1.2 --- Bochner techniques --- p.13 / Chapter 1.3 --- Eigenvalue estimates for Laplacian operator --- p.14 / Chapter 1.4 --- Spectral theory for Schrodinger operator on Rieman- nian manifolds --- p.16 / Chapter 2 --- Vanishing theorems --- p.20 / Chapter 2.1 --- Liouville type theorem for Lp subharmonic functions --- p.20 / Chapter 2.2 --- Generalized type of vanishing theorem --- p.21 / Chapter 3 --- Finite dimensionality results --- p.28 / Chapter 3.1 --- Three types of integral inequalities --- p.28 / Chapter 3.2 --- Weak Harnack inequality --- p.34 / Chapter 3.3 --- Li's abstract finite dimensionality theorem --- p.37 / Chapter 3.4 --- Applications of the finite dimensionality theorem --- p.42 / Chapter 4 --- Ends of Riemannian manifolds --- p.48 / Chapter 4.1 --- Green's function --- p.48 / Chapter 4.2 --- Ends and harmonic functions --- p.53 / Chapter 4.3 --- Some topological applications --- p.72 / Chapter 5 --- Splitting theorems --- p.79 / Chapter 5.1 --- Splitting theorems for manifolds with non-negative Ricci curvature --- p.79 / Chapter 5.2 --- Splitting theorems for manifolds of Ricci curvature with a negative lower bound --- p.83 / Chapter 5.3 --- Manifolds with the maximal possible eigenvalue --- p.93 / Bibliography --- p.102

Ma, Ding. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 59-60). / Abstracts in English and Chinese. / Chapter 1 --- Generalized complex structures --- p.8 / Chapter 1.1 --- Maximal isotropic subspaces of V+ V* --- p.8 / Chapter 1.2 --- Courant bracket --- p.12 / Chapter 1.3 --- Dirac structures --- p.17 / Chapter 1.4 --- Linear generalized complex structures and almost gen- eralized complex structures --- p.19 / Chapter 1.5 --- Integrability conditions --- p.23 / Chapter 2 --- L∞-algebra --- p.25 / Chapter 2.1 --- Original definition of L∞-algebra in terms of lots of brackets --- p.25 / Chapter 2.2 --- Reformulation in terms of differential coalgebra --- p.27 / Chapter 2.3 --- Reformulation in terms of differential algebra --- p.28 / Chapter 2.4 --- Associating T+T* a Lie 2-algebra --- p.29 / Chapter 3 --- Generalized symplectic structures --- p.33 / Chapter 3.1 --- Linear generalized symplectic structures --- p.33 / Chapter 3.2 --- Generalized almost symplectic structures --- p.39 / Chapter 3.3 --- Generalized exterior derivatives and integrability con- ditions --- p.42 / Chapter 3.4 --- Generalized Darboux theorem --- p.45 / Chapter 3.5 --- Generalized Lagrangian submanifolds --- p.46 / Chapter 3.6 --- Generalized moment maps --- p.50 / Chapter 4 --- Generalized Kahler structures --- p.55 / Chapter 4.1 --- Definitions and integrability conditions --- p.55 / Bibliography --- p.59

Thesis (Ph. D.)--Oregon State University, 1980. / Typescript (photocopy). Includes bibliographical references. Also available on the World Wide Web.

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Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 103-106). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (M. Phil.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 100-102).

published_or_final_version / Mathematics / Master / Master of Philosophy