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 ...

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 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 ...

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 ...

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 ...

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 ...

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 ...