RUcore: Rutgers University Community Repository
The convergence theorem of discrete uniformization factors on closed surfaces
Descriptive
TitleInfo
Title
The convergence theorem of discrete uniformization factors on closed surfaces
Name
(type = personal)
NamePart
(type = family)
Zhu
NamePart
(type = given)
Xiaoping
DisplayForm
Xiaoping Zhu
Role
RoleTerm
(authority = RULIB)
author
Name
(type = personal)
NamePart
(type = family)
Luo
NamePart
(type = given)
Feng
DisplayForm
Feng Luo
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
chair
Name
(type = personal)
NamePart
(type = family)
Han
NamePart
(type = given)
Zhengchao
DisplayForm
Zhengchao Han
Affiliation
Advisory Committee
Role
RoleTerm
(authority = local)
member
Name
(type = personal)
NamePart
(type = family)
Sun
NamePart
(type = given)
Hongbin
DisplayForm
Hongbin Sun
Affiliation
Advisory Committee
Role
RoleTerm
(authority = local)
member
Name
(type = personal)
NamePart
(type = family)
Glickenstein
NamePart
(type = given)
David
DisplayForm
David Glickenstein
Affiliation
Advisory Committee
Role
RoleTerm
(authority = local)
member
Name
(type = corporate)
NamePart
Rutgers University
Role
RoleTerm
(authority = RULIB)
degree grantor
Name
(type = corporate)
NamePart
School of Graduate Studies
Role
RoleTerm
(authority = RULIB)
school
TypeOfResource
Text
Genre
(authority = marcgt)
theses
OriginInfo
DateCreated
(encoding = w3cdtf);
(qualifier = exact);
(keyDate = yes)
2022
DateOther
(encoding = w3cdtf);
(type = degree);
(qualifier = exact)
2022-05
Language
LanguageTerm
(authority = ISO 639-3:2007);
(type = text)
English
Abstract
(type = abstract)
In this thesis, we will investigate the convergence of discrete conformal metrics to the classical uniformization metric on Riemannian surfaces. We prove that for a reasonable geodesic triangle mesh on a smooth closed orientable surface, there exists a discrete conformal factor for the induced piecewise linear metric. And the difference between this discrete conformal factor and the classical uniformization factor is controlled by the maximal edge length of the triangulation. The estimates rely on collections of discrete elliptic estimates and isoperimetric inequalities for triangle meshes. The case for genus h >= 1 is a joint work with Tianqi Wu, the case for genus h = 0 is a joint work with Tianqi Wu and Yanwen Luo.
Subject
(authority = RUETD)
Topic
Mathematics
Subject
(authority = local)
Topic
Discrete differential geometry
RelatedItem
(type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
(type = RULIB)
ETD
Identifier
http://dissertations.umi.com/gsnb.rutgers:11820
PhysicalDescription
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
77 pages : illustrations
Note
(type = degree)
Ph.D.
Note
(type = bibliography)
Includes bibliographical references
RelatedItem
(type = host)
TitleInfo
Title
School of Graduate Studies Electronic Theses and Dissertations
Identifier
(type = local)
rucore10001600001
Location
PhysicalLocation
(authority = marcorg);
(displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier
(type = doi)
doi:10.7282/t3-qvx9-6a28
Back to the top
Rights
RightsDeclaration
(ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder
(type = personal)
Name
FamilyName
Zhu
GivenName
Xiaoping
Role
Copyright holder
RightsEvent
Type
Permission or license
DateTime
(encoding = w3cdtf);
(qualifier = exact);
(point = start)
2022-06-06T17:11:09
AssociatedEntity
Name
Xiaoping Zhu
Role
Copyright holder
Affiliation
Rutgers University. School of Graduate Studies
AssociatedObject
Type
License
Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
Back to the top
Technical
RULTechMD
(ID = TECHNICAL1)
ContentModel
ETD
OperatingSystem
(VERSION = 5.1)
windows xp
DateCreated
(point = end);
(encoding = w3cdtf);
(qualifier = exact)
2022-06-06T17:11:10
CreatingApplication
Version
1.5
ApplicationName
xdvipdfmx (20200315)
DateCreated
(point = start);
(encoding = w3cdtf);
(qualifier = exact)
2022-03-31T11:23:16
Back to the top
Statistical Profile