DC FieldValueLanguage
dc.contributor.advisorIzmestiev, Ivan-
dc.contributor.authorProsanov, Roman-
dc.date.accessioned2020-07-23T16:40:26Z-
dc.date.issued2020-
dc.date.submitted2020-06-
dc.identifier.urihttps://doi.org/10.34726/hss.2020.74760-
dc.identifier.urihttp://hdl.handle.net/20.500.12708/15148-
dc.description.abstractThis 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.formatix, 133 Seiten-
dc.languageEnglish-
dc.language.isoen-
dc.subjecthyperbolic 3-manifoldsen
dc.subjectFuchsian manifoldsen
dc.subjectconvex surfacesen
dc.subjectintrinsic metricen
dc.subjectdiscrete curvatureen
dc.subjectdiscrete uniformizationen
dc.titleDiscrete curvature and rigidity of Fuchsian manifoldsen
dc.typeThesisen
dc.typeHochschulschriftde
dc.identifier.doi10.34726/hss.2020.74760-
dc.publisher.placeWien-
tuw.thesisinformationTechnische Universität Wien-
tuw.publication.orgunitE104 - Institut für Diskrete Mathematik und Geometrie-
dc.type.qualificationlevelDoctoral-
dc.identifier.libraryidAC15673257-
dc.description.numberOfPages133-
dc.thesistypeDissertationde
dc.thesistypeDissertationen
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.openaccessfulltextOpen Access-
item.openairetypeThesis-
item.openairetypeHochschulschrift-
item.fulltextwith Fulltext-
item.languageiso639-1en-
item.grantfulltextopen-
item.cerifentitytypePublications-
item.cerifentitytypePublications-
Appears in Collections:Thesis

Files in this item:


Page view(s)

23
checked on Aug 20, 2021

Download(s)

22
checked on Aug 20, 2021

Google ScholarTM

Check


Items in reposiTUm are protected by copyright, with all rights reserved, unless otherwise indicated.