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Curvature flow in hyperbolic spaces

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dc.contributor.authorAndrews, Ben
dc.contributor.authorChen, Xuzhong
dc.date.accessioned2021-06-03T01:34:23Z
dc.date.available2021-06-03T01:34:23Z
dc.date.issued2017
dc.date.updated2020-11-23T10:23:31Z
dc.description.abstractWe study the evolution of compact convex hypersurfaces in hyperbolic space ℍn+1, with normal speed governed by the curvature. We concentrate mostly on the case of surfaces, and show that under a large class of natural flows, any compact initial surface with Gauss curvature greater than 1 produces a solution which converges to a point in finite time, and becomes spherical as the final time is approached. We also consider the higher-dimensional case, and show that under the mean curvature flow a similar result holds if the initial hypersurface is compact with positive Ricci curvature.en_AU
dc.description.sponsorshipThe first author was partly supported by Discovery Projects grant DP1200097 of the Australian Research Council. The second author was partly supported by National Natural Science Foundation of China under grants 11271132, 11071212 and 11131007. The authors are grateful for the hospitality of the Mathematical Sciences Center of Tsinghua University where the research was carried outen_AU
dc.format.mimetypeapplication/pdfen_AU
dc.identifier.issn0075-4102en_AU
dc.identifier.urihttp://hdl.handle.net/1885/236350
dc.language.isoen_AUen_AU
dc.provenancehttps://v2.sherpa.ac.uk/id/publication/23760..."The Published Version can be archived in a Non-Commercial Institutional Repository. 12 months embargo" from SHERPA/RoMEO site (as at 3/06/2021).en_AU
dc.publisherWalter de Gruyteren_AU
dc.rights© De Gruyter 2015en_AU
dc.sourceJournal fur Reine und Angewandte Mathematiken_AU
dc.titleCurvature flow in hyperbolic spacesen_AU
dc.typeJournal articleen_AU
dcterms.accessRightsOpen Accessen_AU
local.bibliographicCitation.lastpage49en_AU
local.bibliographicCitation.startpage29en_AU
local.contributor.affiliationAndrews, Benjamin, College of Science, ANUen_AU
local.contributor.affiliationChen, Xuzhong, East China Normal Universityen_AU
local.contributor.authoruidAndrews, Benjamin, u8610103en_AU
local.description.notesImported from ARIESen_AU
local.identifier.absfor010102 - Algebraic and Differential Geometryen_AU
local.identifier.ariespublicationa383154xPUB4653en_AU
local.identifier.citationvolume729en_AU
local.identifier.doi10.1515/crelle-2014-0121en_AU
local.identifier.scopusID2-s2.0-84990204059
local.identifier.thomsonID000406653700002
local.publisher.urlhttps://www.degruyter.com/view/j/crllen_AU
local.type.statusPublished Versionen_AU

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