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Canonical Kähler metrics with cone singularities
Descriptive
TitleInfo
Title
Canonical Kähler metrics with cone singularities
Name
(type = personal)
NamePart
(type = family)
Datar
NamePart
(type = given)
Ved
NamePart
(type = date)
1987-
DisplayForm
Ved Datar
Role
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author
Name
(type = personal)
NamePart
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Song
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Jian
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Jian Song
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Advisory Committee
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chair
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Chanillo
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Sagun
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Sagun Chanillo
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Advisory Committee
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internal member
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Huang
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Xiaojun
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Xiaojun Huang
Affiliation
Advisory Committee
Role
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internal member
Name
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Wang
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Xiaowei
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Xiaowei Wang
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Advisory Committee
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Rutgers University
Role
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degree grantor
Name
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NamePart
Graduate School - New Brunswick
Role
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school
TypeOfResource
Text
Genre
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theses
OriginInfo
DateCreated
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2014
DateOther
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(type = degree)
2014-05
Place
PlaceTerm
(type = code)
xx
Language
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(type = code)
eng
Abstract
(type = abstract)
This dissertation consists of some results on the existence and regularity of canonical Kähler metrics with cone singularities. First, a much shorter proof is provided for a result of H. Guenancia and M. Paun, that solutions to some complex Monge-Ampère equations with conical singularities along effective simple normal crossing divisors are uniformly equivalent to a conical metric along that divisor. It is also shown that such metrics can always be approximated, in the Gromov-Hausdorff topology, by smooth metrics with a uniform Ricci lower bound and uniform diameter bound. As an application, it is proved that the regular set of these metrics is convex. Next, the existence of conical Kähler-Einstein metrics and conical Kähler-Ricci solitons on toric manifolds is studied in relation to the greatest lower bounds for the Ricci and the Bakry-Emery Ricci curvatures. It is also shown that any two toric manifolds of the same dimension can be connected by a continuous path of toric manifolds with conical Kähler-Einstein metrics in the Gromov-Hausdorff topology. In the final chapter, the greatest lower bound for the Bakry-Emery Ricci curvature is studied on Fano manifolds. In particular, it is related to the solvability of some soliton-type complex Monge-Ampère equations and the properness of a twisted Mabuchi energy, extending previous work of Székelyhidi on the greatest lower bound for Ricci curvature.
Subject
(authority = RUETD)
Topic
Mathematics
Subject
(authority = ETD-LCSH)
Topic
Kählerian manifolds
Subject
(authority = ETD-LCSH)
Topic
Kählerian structures
Subject
(authority = ETD-LCSH)
Topic
Manifolds (Mathematics)
RelatedItem
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
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ETD
RelatedItem
(type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier
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rucore19991600001
Identifier
ETD_5481
Identifier
(type = doi)
doi:10.7282/T3571996
PhysicalDescription
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electronic resource
InternetMediaType
application/pdf
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text/xml
Extent
vii, 99 p. : ill.
Note
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Ph.D.
Note
(type = bibliography)
Includes bibliographical references
Location
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(displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Note
(type = statement of responsibility)
by Ved V. Datar
Genre
(authority = ExL-Esploro)
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
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Datar
GivenName
Ved
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime
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2014-04-14 00:02:39
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Name
Ved Datar
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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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ETD
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windows xp
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