Polynomial growth harmonic diffeomorphisms from complex plane into hyperbolic plane.

Chan Mei Shan.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.Includes bibliographical references (leaves 74-76).Abstracts in English and Chinese.Chapter 0 --- Introduction --- p.1Chapter 1 --- Preliminary --- p.9Chapter 1.1 --- Harmonic maps between Riemann Surfaces --- p.9Chapter 1.2 --- "Minkowski 3-spaces, M21" --- p.17Chapter 1.3 --- Preliminaries from analysis --- p.21Chapter 2 --- Holomorphic quadratic differentials --- p.27Chapter 2.1 --- Solution on the Poincare disk D --- p.28Chapter 2.2 --- Solution on the complex plane C --- p.37Chapter 3 --- Harmonic Diffeomorphisms into H2 --- p.46Chapter 3.1 --- The case from D onto D --- p.46Chapter 3.2 --- Open harmonic embeddings from C into H --- p.53Chapter 4 --- Open harmonic embeddings with polynomial Hopf differentials --- p.57Chapter 4.1 --- Proof of the theorem --- p.58Chapter 4.2 --- Open harmonic embeddings on C with fixed ideal polygonal images in H2 --- p.65Bibliography --- p.7