Some existence and uniqueness results of harmonic maps
Author
Mou, Libin H.
Date
1990Advisor
Hardt, Robert M.
Degree
Doctor of Philosophy
Abstract
This thesis discusses some existence and uniqueness problems of harmonic maps. It consists of two parts: Part I. Existence of harmonic maps with prescribed finite singularities. Here we address the question of existence of a harmonic map from a spatial domain to the sphere S$\sp2$ which has a prescribed finite set of singularities.
Part II. Uniqueness of energy minimizing harmonic maps for almost all smooth boundary data. Suppose $\Omega$ is a smooth domain in R$\sp{m}$ and N is a compact smooth manifold. Here we show roughly that almost all smooth maps from $\partial\Omega$ to N serve as boundary values for a unique energy minimizing map u from $\Omega$ to N. This involves constructing a finite measure on a suitable (infinite dimensional) space of smooth boundary values.
Keyword
Mathematics