PLEASE WAIT, LOADING...
Loading ...
ProQuest

Citation/Abstract

Properties of the Gauss-Green form on the moduli space of unduloids


2008 2008

Other formats: Order a copy

Abstract (summary)


In this work, we examine the moduli space of unduloids. This space parametrizes the asymptotic behavior of the ends of properly Alexandrov embedded, CMC (constant mean curvature) surfaces of finite topology. In particular, we examine the Gauss-Green form, a natural 2-form on this moduli space. Using coordinate expressions, derived in the appendices, for the Jacobi functions on an unduloid, we derive a coordinate expression for the Gauss-Green form, proving it to be a non-closed, almost-symplectic (i.e. non-degenerate) form. Finally, we outline a path for further study involving the Gromov Compactness Theorem.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences, Constant mean curvature, Curvature surface, Unduloid moduli, Gauss-Green form, Moduli space, Unduloids
Title
Properties of the Gauss-Green form on the moduli space of unduloids
Author
Damon, Eli
Number of pages
54
Publication year
2008
Degree date
2008
School code
0118
Source
DAI-B 69/08, Feb 2009
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780549663768
Advisor
Kusner, Robert
Committee member
Gunnells, Paul, Sullivan, Michael, Kastor, David
University/institution
University of Massachusetts Amherst
Department
Mathematics
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3315498
ProQuest document ID
219982005
Copyright
Copyright ProQuest, UMI Dissertations Publishing 2008
Document URL
http://search.proquest.com/docview/219982005