<div class="csl-bib-body">
<div class="csl-entry">Prosanov, R. (2020). <i>Discrete curvature and rigidity of Fuchsian manifolds</i> [Dissertation, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2020.74760</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2020.74760
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/15148
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dc.description.abstract
This thesis is devoted to some applications of cone-manifolds and discrete curvature to problems in 3-dimensional hyperbolic geometry. First, we prove a realization and rigidity result for a specific family of hyperbolic cone-3-manifolds. This allows us to give a new variational proof of the existence and uniqueness of a hyperbolic cone-metric on S_g with prescribed curvature in a given discrete conformal class. Here S_g is a closed orientable surface of genus g > 1. This also provides a new proof of the fact that every hyperbolic cusp-metric on S_g can be uniquely realized as a convex surface in a Fuchsian manifold. A Fuchsian manifold is a hyperbolic manifold homeomorphic to S_g ×[0; +∞) with geodesic boundary Sg × {0}. They are known as toy cases for studying geometry of non-compact hyperbolic 3-manifolds and hyperbolic 3-manifolds with boundary. Second, we consider compact Fuchsian manifolds with boundary, i.e., hyperbolic manifolds homeomorphic to S_g × [0; 1] with geodesic boundary S_g × {0}. We use cone-manifolds to prove that a compact Fuchsian manifold with convex boundary is uniquely determined by the induced metric on S_g × {1}. It is distinguishing that except convexity we do not put any other condition on the boundary, so it may be neither smooth nor polyhedral.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
hyperbolic 3-manifolds
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dc.subject
Fuchsian manifolds
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dc.subject
convex surfaces
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dc.subject
intrinsic metric
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dc.subject
discrete curvature
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dc.subject
discrete uniformization
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dc.title
Discrete curvature and rigidity of Fuchsian manifolds
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dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2020.74760
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Roman Prosanov
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dc.publisher.place
Wien
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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tuw.publication.orgunit
E104 - Institut für Diskrete Mathematik und Geometrie
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dc.type.qualificationlevel
Doctoral
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dc.identifier.libraryid
AC15673257
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dc.description.numberOfPages
133
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dc.thesistype
Dissertation
de
dc.thesistype
Dissertation
en
tuw.author.orcid
0000-0002-0002-8877
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dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
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tuw.advisor.orcid
0000-0003-3173-7841
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item.languageiso639-1
en
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item.mimetype
application/pdf
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item.openairecristype
http://purl.org/coar/resource_type/c_db06
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item.fulltext
with Fulltext
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item.openairetype
doctoral thesis
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item.grantfulltext
open
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item.openaccessfulltext
Open Access
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item.cerifentitytype
Publications
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crisitem.author.dept
E104-03 - Forschungsbereich Differentialgeometrie und geometrische Strukturen
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crisitem.author.parentorg
E104 - Institut für Diskrete Mathematik und Geometrie