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Boundary and Holder regularities of Douady-Earle extensions and eigenvalues of Laplace operators acting on Riemann surfaces

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Title
Boundary and Holder regularities of Douady-Earle extensions and eigenvalues of Laplace operators acting on Riemann surfaces
Name (type = personal)
NamePart (type = family)
Pal
NamePart (type = given)
Susovan
NamePart (type = date)
1983-
DisplayForm
Susovan Pal
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Luo
NamePart (type = given)
Feng
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Feng Luo
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Advisory Committee
Role
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chair
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NamePart (type = family)
Gilman
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Jane
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Jane Gilman
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Advisory Committee
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internal member
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Li
NamePart (type = given)
YanYan
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YanYan Li
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Advisory Committee
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RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Hu
NamePart (type = given)
Jun
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Jun Hu
Affiliation
Advisory Committee
Role
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outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - New Brunswick
Role
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school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (qualifier = exact)
2013
DateOther (qualifier = exact); (type = degree)
2013-10
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
Douady-Earle extensions of homeomorphisms of the unit circle are of particular interest in understanding contractibility and complex structures of Teichmueller and assymptotic Teichmueller spaces. Motivated by questions in analysis and partial differential equations, one can ask how regular the Douady-Earle extensions can be on the closed unit disk if one puts sufficient regularity on the circle homeomorphisms to start with. In first part of this thesis which consists of the first four chapters, we prove that Douady-Earle extensions of Holder continuous circle homeomorphisms are Holder continuous with the same Holder exponent, and Douady-Earle extensions of circle diffeomorphisms are diffeomorphisms of the closed unit disk. Eigenvalues of Laplace operators on Riemannian manifolds are widely studied by differential geometers. But when the manifold is a hyperbolic Riemann surface, the problem becomes more special, because the collar lemma and the minimax principles allow us to construct functions which produce lower and upper bounds on eigenvalues on that Riemann surface. In the second part of this thesis consisting of chapters 5 and 6, we show, using the minimax principles, given any small positive number epsilon and given any big natural number k, we can construct a Riemann surface whose k-th eigenvalue is less than epsilon. The result was first proved by Burton randol, here we provide a much simpler and geometric proof
Subject (authority = RUETD)
Topic
Mathematics
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_4930
PhysicalDescription
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electronic resource
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application/pdf
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text/xml
Extent
vii, 36 p. : ill.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = vita)
Includes vita
Note (type = statement of responsibility)
by Susovan Pal
Subject (authority = ETD-LCSH)
Topic
Riemann surfaces
Subject (authority = ETD-LCSH)
Topic
Teichm├╝ller spaces
Subject (authority = ETD-LCSH)
Topic
Homeomorphisms
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T3S46Q0K
Genre (authority = ExL-Esploro)
ETD doctoral
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The author owns the copyright to this work.
RightsHolder (type = personal)
Name
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Pal
GivenName
Susovan
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2013-07-31 15:04:30
AssociatedEntity
Name
Susovan Pal
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
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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.
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windows xp
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