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Controlled geometry via volumes on Alexandrov spaces

## Descriptive

TypeOfResource
Text
TitleInfo (ID = T-1)
Title
Controlled geometry via volumes on Alexandrov spaces
Identifier
ETD_2554
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000056482
Language
LanguageTerm (authority = ISO639-2); (type = code)
eng
Genre (authority = marcgt)
theses
Subject (ID = SBJ-1); (authority = RUETD)
Topic
Mathematics
Subject (ID = SBJ-2); (authority = ETD-LCSH)
Topic
Geodesics (Mathematics)
Subject (ID = SBJ-3); (authority = ETD-LCSH)
Topic
Geometry, Differential
Subject (ID = SBJ-4); (authority = ETD-LCSH)
Topic
Rigidity (Geometry)
Abstract (type = abstract)
In this thesis we recall the basic definitions and properties for Alexandrov space and describe two geometry phenomenons controlled via volume (Hausdorff measure or rough volume) conditions. (1) For a path in X [Greek letter epsilon] 2 Alex [superscript n] (Greek letter kappa) (the compact n-dimensional Alexandrov spaces with curvature [greater than or equal to kappa].), the sum of the length and the turning angle is bounded from below in terms of [kappa], n, diameter and volume of X. This generalizes a basic estimate by Cheeger on the length of a closed geodesic in closed Riemannian manifold ([Ch]). (2) Let [epsilon]p be the space of directions at p 2 [epsilon] X and the pointed radius R = inf{r : X C B[subscript r](p)}. If X [epsilon] Alex[superscript n](kappa), then vol(X) [less than or equal to symbol] vol(CR/k (Epsilon subscript p). where (CR/k (Epsilon subscript p) is the metric R-ball at the vertex in the [kappa]-suspension (CR/k (Epsilon subscript p). We give an isometric classification of X X [epsilon] Alex[superscript n](kappa) whose volume achieves the maximal possible value (CR/k (Epsilon subscript p). We also determine homeomorphic types of such X when X is a topological manifold. These results are natural extension of K. Grove and P. Petersen's work in 1992 ([GP 92]).
PhysicalDescription
Form (authority = gmd)
electronic resource
Extent
vi, 90 p. : ill.
InternetMediaType
application/pdf
InternetMediaType
text/xml
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = vita)
Includes vita
Note (type = statement of responsibility)
by Nan Li
Name (ID = NAME-1); (type = personal)
NamePart (type = family)
Li
NamePart (type = given)
Nan
NamePart (type = date)
1980-
Role
RoleTerm (authority = RULIB)
author
DisplayForm
Nan Li
Name (ID = NAME-2); (type = personal)
NamePart (type = family)
Rong
NamePart (type = given)
Xiaochun
Role
RoleTerm (authority = RULIB)
chair
Affiliation
DisplayForm
Xiaochun Rong
Name (ID = NAME-3); (type = personal)
NamePart (type = family)
Luo
NamePart (type = given)
Feng
Role
RoleTerm (authority = RULIB)
internal member
Affiliation
DisplayForm
Feng Luo
Name (ID = NAME-4); (type = personal)
NamePart (type = family)
Han
NamePart (type = given)
Zhengchao
Role
RoleTerm (authority = RULIB)
internal member
Affiliation
DisplayForm
Zhengchao Han
Name (ID = NAME-5); (type = personal)
NamePart (type = family)
Cao
NamePart (type = given)
Jianguo
Role
RoleTerm (authority = RULIB)
outside member
Affiliation
DisplayForm
Jianguo Cao
Name (ID = NAME-1); (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (ID = NAME-2); (type = corporate)
NamePart
Role
RoleTerm (authority = RULIB)
school
OriginInfo
DateCreated (qualifier = exact)
2010
DateOther (qualifier = exact); (type = degree)
2010-10
Place
PlaceTerm (type = code)
xx
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Identifier (type = doi)
doi:10.7282/T37944FC
Genre (authority = ExL-Esploro)
ETD doctoral
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## Rights

RightsDeclaration (AUTHORITY = GS); (ID = rulibRdec0006)
The author owns the copyright to this work.
Status
Availability
Status
Open
Reason
RightsHolder (ID = PRH-1); (type = personal)
Name
FamilyName
Li
GivenName
Nan
Role
RightsEvent (ID = RE-1); (AUTHORITY = rulib)
Type
DateTime
2010-05-13 23:03:53
AssociatedEntity (ID = AE-1); (AUTHORITY = rulib)
Role
Name
Nan Li
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject (ID = AO-1); (AUTHORITY = rulib)
Type
Name
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.
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## Technical

ContentModel
ETD
MimeType (TYPE = file)
application/pdf
MimeType (TYPE = container)
application/x-tar
FileSize (UNIT = bytes)
686080
Checksum (METHOD = SHA1)
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