Wong, Yat Sen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 71-72). / Abstract also in Chinese. / Chapter 1 --- Lorentz Manifolds --- p.6 / Chapter 1.1 --- Preliminaries --- p.6 / Chapter 1.2 --- "Parallel Translation, geodesics and exponential map" --- p.9 / Chapter 1.3 --- "Curvature, frame field and Ricci curvature" --- p.14 / Chapter 1.4 --- Two-parameter maps --- p.15 / Chapter 2 --- Causal character in Lorentz geometry --- p.17 / Chapter 2.1 --- The Gauss Lemma --- p.17 / Chapter 2.2 --- Local causal character --- p.19 / Chapter 2.3 --- Timecones --- p.20 / Chapter 2.4 --- Local Lorentz Geometry --- p.21 / Chapter 3 --- Calculus of variations --- p.24 / Chapter 3.1 --- Jacobi fields --- p.24 / Chapter 3.2 --- Lorentz submanifolds --- p.25 / Chapter 3.3 --- The endmanifold case --- p.26 / Chapter 3.4 --- Focal points --- p.27 / Chapter 3.5 --- A causality theorem --- p.28 / Chapter 4 --- Causality in Lorentz manifolds --- p.32 / Chapter 4.1 --- Causality relations --- p.32 / Chapter 4.2 --- Quasi-limits --- p.35 / Chapter 4.3 --- Causality conditions --- p.37 / Chapter 4.4 --- Time separation --- p.39 / Chapter 4.5 --- Achronal sets --- p.42 / Chapter 4.6 --- Cauchy hypersurfaces --- p.43 / Chapter 4.7 --- Cauchy developments --- p.45 / Chapter 4.8 --- Spacelike hypersurfaces --- p.49 / Chapter 4.9 --- Cauchy horizons --- p.52 / Chapter 4.10 --- Hawking´ةs Singularity Theorem --- p.56 / Chapter 4.11 --- Penrose´ةs Singularity Theorem --- p.58 / Chapter 5 --- "Monge-Ampere equations, the Bergman kernel, and geometry of pesudoconvex domains" --- p.62 / Chapter 5.1 --- Monge-Ampere equations --- p.62 / Chapter 5.2 --- Differential geometry on the boundary --- p.63 / Chapter 5.3 --- Computations --- p.66 / Bibliography --- p.71
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326709 |
| Date | January 2009 |
| Contributors | Wong, Yat Sen., 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, 72 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 0.0018 seconds