by Lei Ka Keung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 70-71). / Abstracts in English and Chinese. / Chapter 0 --- Introduction --- p.5 / Chapter 1 --- Dirichlet Problem at infinity --- p.9 / Chapter 1.1 --- The Geometric Boundary --- p.9 / Chapter 1.2 --- Dirichlet Problem --- p.15 / Chapter 2 --- The Martin Boundary --- p.29 / Chapter 2.1 --- The Martin Metric --- p.30 / Chapter 2.2 --- The Representation Formula --- p.31 / Chapter 2.3 --- Uniqueness of Representation --- p.36 / Chapter 3 --- The Geometric boundary and the Martin boundary --- p.42 / Chapter 3.1 --- Estimates for harmonic functions in cones --- p.42 / Chapter 3.2 --- A Harnack Inequality at Infinity --- p.49 / Chapter 3.3 --- The kernel function --- p.54 / Chapter 3.4 --- The Main Theorem --- p.55 / Chapter 4 --- Positive Harmonic Functions on Product of Manifolds --- p.61 / Chapter 4.1 --- Splitting Theorem --- p.61 / Chapter 4.2 --- Riemannian Halfspace and the parabolic Martin boundary --- p.62 / Chapter 4.3 --- Splitting of parabolic Martin kernels --- p.63 / Chapter 4.4 --- Proof of theorem 4.1 --- p.66 / Bibliography
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_322664 |
| Date | January 1999 |
| Contributors | Lei, Ka Keung., 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, 71 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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