Ip Tsz Ho. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 86-89). / Chapter 0 --- Introduction --- p.5 / Chapter 1 --- Preliminary --- p.11 / Chapter 1.1 --- Background in analysis --- p.11 / Chapter 1.1.1 --- Holder Continuity --- p.11 / Chapter 1.1.2 --- Hausdorff Measure --- p.12 / Chapter 1.1.3 --- Weak Derivatives --- p.13 / Chapter 1.2 --- Basic Facts of Harmonic Functions --- p.14 / Chapter 1.2.1 --- Harmonic Approximation --- p.14 / Chapter 1.2.2 --- Elliptic Regularity --- p.15 / Chapter 1.3 --- Background in geometry --- p.16 / Chapter 1.3.1 --- Notations and Symbols --- p.16 / Chapter 1.3.2 --- Nearest Point Projection --- p.16 / Chapter 2 --- Monotonicity formula and Regularity of Harmonic maps --- p.17 / Chapter 2.1 --- Energy Minimizing Maps --- p.17 / Chapter 2.2 --- Variational Equations --- p.18 / Chapter 2.3 --- Monotonicity Formula --- p.21 / Chapter 2.4 --- A Technical Lemma --- p.22 / Chapter 2.5 --- Luckhau's Lemma --- p.28 / Chapter 2.6 --- Reverse Poincare Inequality --- p.40 / Chapter 2.7 --- ε-Regularity of Energy Minimizing Maps --- p.45 / Chapter 3 --- Monotonicity Formulae and Vanishing Theorems --- p.52 / Chapter 3.1 --- Stress energy tensor and basic formulae for harmonic p´ؤforms --- p.52 / Chapter 3.2 --- Monotonicity formula --- p.59 / Chapter 3.2.1 --- Monotonicity Formula for Harmonic Maps --- p.64 / Chapter 3.2.2 --- Bochner-Weitzenbock Formula --- p.65 / Chapter 3.3 --- Conservation Law and Vanishing Theorem --- p.68 / Chapter 4 --- On conformally compact Einstein Manifolds --- p.71 / Chapter 4.1 --- Energy Decay of Harmonic Maps with Finite Total Energy --- p.73 / Chapter 4.2 --- Vanishing Theorem of Harmonic Maps --- p.81 / Bibliography --- p.86
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_324110 |
| Date | January 2002 |
| Contributors | Ip, Tsz Ho., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, 89 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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