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Critical Riemannian metrics
(1990)
Let $(M,g)$ be a compact oriented n-dimensional smooth Riemannian manifold. Consider the following quadratic Riemannian functional$$SR(g) = \int\sb{M}\ \vert R\sb{ijkl}(g)\vert \sp{2}d\mu$$which is homogeneous of degree ...
Stability and regularity of an inverse elliptic boundary value problem
(1990)
The inverse conductivity problem is that of recovering a spatially varying isotropic conductivity in the interior of some bounded region by means of steady-state measurements taken only at the boundary. In the underlying ...
Cone manifolds in three-dimensional topology applications to branched covers
(1990)
Cone manifolds are defined and several standard geometric techniques for Riemannian manifolds are generalized to this setting.
Smoothing techniques for approximating cone manifolds by smooth Riemannian manifolds with bounded ...
Fully transitive polyhedra with crystallographic symmetry groups
(1990)
This dissertation sets forth a method for classifying, up to euclidean similarity, fully-transitive polyhedra which have crystallographic symmetry groups. Branko Grunbaum's definition of polyhedron is used, in which the ...
Surface mapping classes and Heegaard decompositions of 3-manifolds
(1990)
The thesis is constituted in two parts. The first part including the first four chapters concentrates on the surface mapping class groups. The second part including the last three chapters focuses on their applications in ...
Some existence and uniqueness results of harmonic maps
(1990)
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 ...
A robust trust region algorithm for nonlinear programming
(1990)
This paper develops and tests a trust region algorithm for the nonlinear equality constrained optimization problem. Our goal is to develop a robust algorithm that can handle lack of second-order sufficiency away from the ...