Abstract/Details

Geometric Realizations of Cyclically Branched Coverings over Punctured Spheres

Lee, Dami.  Indiana University. ProQuest Dissertations Publishing, 2018. 10845072.

Abstract (summary)

In classical differential geometry, a central question has been whether abstract surfaces with given geometric features can be realized as surfaces in Euclidean space. Inspired by the rich theory of embedded triply periodic minimal surfaces, we seek examples of triply periodic polyhedral surfaces that have an identifiable conformal structure. In particular we are interested in explicit cone metrics on compact Riemann surfaces that have a realization as the quotient of a triply periodic polyhedral surface. This is important as Riemann surfaces where one has equivalent descriptions are rare. We construct periodic surfaces using graph theory as an attempt to make Schoen's heuristic concept of a dual graph rigorous. We then combine the theory of cyclically branched coverings over punctured spheres to identify the conformal type of each surface.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Geometry; Surfaces
Title
Geometric Realizations of Cyclically Branched Coverings over Punctured Spheres
Author
Lee, Dami  VIAFID ORCID Logo 
Number of pages
94
Degree date
2018
School code
0093
Source
DAI-B 80/01(E), Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
978-0-438-30352-2
Advisor
Weber, Matthias
Committee member
Bainbridge, Matthew; Solomon, Bruce; Thurston, Dylan
University/institution
Indiana University
Department
Mathematics
University location
United States -- Indiana
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
10845072
ProQuest document ID
2099567874
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/2099567874