by Pun Shu Hoi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1990. / Bibliography: leaves 124-128. / Abstract --- p.1 / Acknowledgement --- p.2 / Introduction --- p.3 / Chapter I --- On the omitted values of the Gauss map of complete minimal surfaces --- p.8 / Chapter 1 --- Weierstrass Representation of minimal surface --- p.9 / Chapter 1.1 --- The generalized Gauss Map --- p.9 / Chapter 1.2 --- Gauss map in R3 --- p.13 / Chapter 1.3 --- Gauss map in R4 --- p.18 / Chapter 2 --- An optimal result on the omitted values --- p.23 / Chapter 2.1 --- Xavier's result --- p.23 / Chapter 2.2 --- A lower bound for Poincare metric --- p.32 / Chapter 2.3 --- A function-theoretic lemma --- p.37 / Chapter 2.4 --- The optimal result --- p.43 / Chapter 3 --- The relation between omitted values and total curvature --- p.57 / Chapter 3.1 --- An extension of Xavier's result --- p.57 / Chapter 3.2 --- An extension of Fujimoto's Theorem --- p.65 / Chapter II --- On geometry of complete minimal surfaces with finite Morse index in 3-manifold of non-negative scalar curvature --- p.75 / Chapter 4 --- The structure of complete stable minimal surfaces in3- manifolds of non-negative scalar curvature --- p.76 / Chapter 4.1 --- Preliminary results on λi of the operator Δ ´ؤ q --- p.76 / Chapter 4.2 --- Some results on the operator Δ ´ؤ ak for conformal metrics on the disk --- p.81 / Chapter 4.3 --- Classification Theorem --- p.86 / Chapter 4.4 --- Complete stable minimal surfaces in complete scalar flat 3- manifolds --- p.92 / Chapter 5 --- On complete minimal surfaces with finite Morse index in 3-manifolds of non-negative scalar curvature --- p.96 / Chapter 5.1 --- On properties of the operator L --- p.96 / Chapter 5.2 --- The geometry of minimal surfaces of finite index --- p.110 / Chapter 5.3 --- Finite index minimal sufrace in R3 --- p.120 / Bibliography --- p.124
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_318632 |
| Date | January 1990 |
| Contributors | Pun, Shu Hoi., 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, 128 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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