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
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_320523 |
| Date | January 1995 |
| Contributors | Leung, Kwok Kei., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Publisher | Chinese University of Hong Kong |
| Source Sets | The Chinese University of Hong Kong |
| Language | English |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, ii, 94 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/) |
Page generated in 0.0016 seconds