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Scalar curvature rigidity on locally conformally flat manifolds with boundary

dc.contributor.advisorBallmann, Werner
dc.contributor.authorSpiegel, Fabian-Michael
dc.date.accessioned2020-04-23T01:37:43Z
dc.date.available2020-04-23T01:37:43Z
dc.date.issued21.12.2016
dc.identifier.urihttp://hdl.handle.net/20.500.11811/6945
dc.description.abstractInspired by the work of F. Hang and X. Wang and partial results by S. Raulot, we prove a scalar curvature rigitidy result for locally conformally flat manifolds with boundary in the spirit of the well-known Min-Oo conjecture. Our results imply that Min-Oo’s conjecture is true provided the considered manifold is locally conformally flat. In exchange, we require less knowledge on the geometry of the boundary than in the original statement of Min-Oo’s conjecture. Furthermore, our result can be extended to yield a similar rigidity result for geodesic balls in a hemisphere.
Applications of our techniques include rigidity results for more general domains in a hemisphere and geodesic balls in Euclidean space as well as an extension of our result to locally conformally symmetric manifolds. To that end, we additionally establish that our results are valid for manifolds with parallel Ricci tensor, under slightly stronger assumptions on the geometry of the boundary.
dc.language.isoeng
dc.rightsIn Copyright
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectRiemannsche Geometrie
dc.subjectStarrheit
dc.subjectRandwertprobleme auf Mannigfaltigkeiten
dc.subjectSkalarkrümmung
dc.subjectMin-Oo-Vermutung
dc.subjectGlobal Riemannian geometry
dc.subjectRigidity
dc.subjectBoundary value problems on manifolds
dc.subjectScalar curvature
dc.subjectMin-Oo Conjecture
dc.subject.ddc510 Mathematik
dc.titleScalar curvature rigidity on locally conformally flat manifolds with boundary
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
dc.publisher.locationBonn
dc.rights.accessRightsopenAccess
dc.identifier.urnhttps://nbn-resolving.org/urn:nbn:de:hbz:5n-45785
ulbbn.pubtypeErstveröffentlichung
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.affiliation.locationBonn
ulbbnediss.thesis.levelDissertation
ulbbnediss.dissID4578
ulbbnediss.date.accepted2016-11-22
ulbbnediss.instituteMathematisch-Naturwissenschaftliche Fakultät : Fachgruppe Mathematik / Mathematisches Institut
ulbbnediss.fakultaetMathematisch-Naturwissenschaftliche Fakultät
dc.contributor.coRefereeMüller, Werner


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