## Search

Now showing items 1-10 of 61

#### 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 ...

#### Energy minimizers, gradient flow solutions, and computational investigations in the theory of biharmonic maps

(1998)

We present the definitions, derive the relevant Euler-Lagrange equations, and establish various properties concerning biharmonic maps. We investigate several classes of examples exhibiting singular behavior. Existence of ...

#### A global convergence theory for a general class of trust region algorithms for equality constrained optimization

(1993)

This work is concerned with global convergence results for a broad class of trust region sequential quadratic programming algorithms for the smooth nonlinear programming problem with equality constraints. The family of ...

#### Anomalies in finite dimensions

(1993)

A problem in quantum mechanics is finding a determinant function on linear maps between two vector spaces. In this paper we consider the question in the context of finite dimensional vector spaces. Given two finite dimensional ...

#### Generalized billiard paths and Morse theory for manifolds with corners

(1999)

A billiard path on a manifold M embedded in Euclidean space is a series of line segments connecting reflection points on M. In a generalized billiard path we also allow the path to pass through M. The two segments at a ...

#### Can you hear the size of the vertices? An inverse spectral problem of Laplacians on weighted graphs

(1998)

Let G be a simple graph with n vertices. We define a Laplacian $\Delta$ on G which depends on an assignment of a weight to each vertex of G. One of the eigenvalues of $\Delta$ will always be 0. We fix the remaining (n $-$ ...

#### Harmonic maps of trivalent trees

(1991)

This thesis is a study of harmonic maps of trivalent trees into Euclidean space. The existence of such maps is established, and uniqueness is shown to hold up to a certain isotopy condition. Moreover, within its particular ...

#### An abstract analysis of differential semblance optimization

(1994)

Differential Semblance Optimization (DSO) is a novel way of approaching a class of inverse problems arising in exploration seismology. The promising feature of the DSO method is that it replaces a nonsmooth, highly nonconvex ...

#### Morse-Bott functions and the Witten Laplacian

(1997)

Given a compact Riemannian manifold (N, g), a flat vector bundle V over N, and a Morse-Bott function h, Witten considered the following one-parameter deformation of the differential d in the de Rham complex of V-valued ...

#### Hyperbolic geometry, regular representations and curves on surfaces

(1995)

Tools and techniques in hyperbolic geometry are developed and applied primarily to questions about intersections of curves on surfaces. Formulae which explicitly relate the coefficients of a matrix to the geometric data ...