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Yamabe problem on compact manifolds with boundary
Descriptive
TitleInfo
Title
Yamabe problem on compact manifolds with boundary
Name
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NamePart
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Sun
NamePart
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Liming
NamePart
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1986-
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Liming Sun
Role
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author
Name
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Li
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YanYan
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YanYan Li
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Advisory Committee
Role
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chair
Name
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Han
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Zheng-Chao
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Zheng-Chao Han
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Advisory Committee
Role
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internal member
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Sesum
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Natasa
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Natasa Sesum
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Advisory Committee
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internal member
Name
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NamePart
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Sire
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Yannick
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Yannick Sire
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Advisory Committee
Role
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outside member
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Rutgers University
Role
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degree grantor
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Graduate School - New Brunswick
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school
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Text
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theses
OriginInfo
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2017
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2017-05
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2017
Place
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xx
Language
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eng
Abstract
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We proved the existence of conformal metric with nonzero constant scalar curvature and nonzero constant boundary mean curvature under some natural conditions. We also solved some remaining cases left open by J. Escobar. Furthermore, we establish the compactness of minimizers which led to a partial affirmative answer to the Han-Li conjecture. We also studied one types of Yamabe flow on compact manifolds with boundary, which has mean curvature equals to zero on the boundary. Convergence of flow is established under some conditions. In another work, We studied the classification of nonnegative solutions to polyharmonic functions with conformally invariant boundary conditions. We proved that nonnegative solutions of that elliptic equations have to be of the ``polynomials plus bubbles" form. The presence of a polynomial part is a new phenomenon.
Subject
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Topic
Mathematics
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Title
Rutgers University Electronic Theses and Dissertations
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ETD_7901
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electronic resource
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Extent
1 online resource (vii, 165 p. : ill.)
Note
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Ph.D.
Note
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Includes bibliographical references
Note
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by Liming Sun
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TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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NjNbRU
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doi:10.7282/T3KW5JXZ
Genre
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ETD doctoral
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Rights
RightsDeclaration
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The author owns the copyright to this work.
RightsHolder
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Name
FamilyName
Sun
GivenName
Liming
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime
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2017-04-05 20:48:21
AssociatedEntity
Name
Liming Sun
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
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
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Technical
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windows xp
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2017-04-06T00:20:24
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2017-04-06T00:20:24
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