Physical Sciences and Mathematics Commons^™

Minimal Surfaces And The Weierstrass-Enneper Representation, Evan Snyder

Electronic Theses, Projects, and Dissertations

The field of minimal surfaces is an intriguing study, not only because of the exotic structures that these surfaces admit, but also for the deep connections among various mathematical disciplines. Minimal surfaces have zero mean curvature, and their parametrizations are usually quite complicated and nontrivial. It was shown however, that these exotic surfaces can easily be constructed from a careful choice of complex-valued functions, using what is called the Weierstrass-Enneper Representation.

In this paper, we develop the necessary tools to study minimal surfaces. We will prove some classical theorems and solve an interesting problem that involves ruled surfaces. We will …

Hyperbolic Triangle Groups, Sergey Katykhin

Electronic Theses, Projects, and Dissertations

This paper will be on hyperbolic reflections and triangle groups. We will compare hyperbolic reflection groups to Euclidean reflection groups. The goal of this project is to give a clear exposition of the geometric, algebraic, and number theoretic properties of Euclidean and hyperbolic reflection groups.