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
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_327139 |
| Date | January 2010 |
| Contributors | Wu, Lijiang., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, 105 leaves ; 30 cm. |
| Rights | Use 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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