Dissertation/Thesis Abstract

An Introduction to Discrete Minimal Surfaces via the Enneper Surface
by Hao, Shuai, M.S., Southern Illinois University at Edwardsville, 2013, 49; 1543912
Abstract (Summary)

In this paper, we are exploring how to construct a discrete minimal surface. We map the conformal curvature lines of a parameterized continuous minimal surface to a unit sphere by the Gauss map. Then, based on a circle patterns we create, the Koebe polyhedron can be obtained. By dualizing the Koebe polyhedron, we are able to get the discrete minimal surface. Moreover, instead of only developing the method theoretically, we also show concrete procedures visually by Mathematica for Enneper with arbitrary domain. This is an expository project mainly based on the paper "Minimal surface from circle patterns: geometry from combinatorics" by Alexander I. Bobenko, Tim Hoffmann and Boris A. Springborn.

Indexing (document details)
Advisor: Weyhuapt, Adam G.
Commitee: Lu, Chunqing, Parish, James L.
School: Southern Illinois University at Edwardsville
Department: Mathematics and Statistics
School Location: United States -- Illinois
Source: MAI 52/02M(E), Masters Abstracts International
Subjects: Mathematics
Keywords: Catenoid, Cell decomposition, Christoffel dual, Discrete christoffel dual, Discrete minimal surface, Enneper, Gauss map, Koebe polyhedron, Minimal surface
Publication Number: 1543912
ISBN: 978-1-303-32425-3
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