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Curvature contraction of convex hypersurfaces by nonsmooth speeds

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dc.contributor.authorAndrews, Ben
dc.contributor.authorHolder, Andrew
dc.contributor.authorMcCoy, James
dc.contributor.authorWheeler, Glen
dc.contributor.authorWheeler, Valentina-Mira
dc.contributor.authorWilliams, Graham
dc.date.accessioned2014-12-02T23:29:55Z
dc.date.issued2014-09
dc.date.updated2015-12-08T08:56:30Z
dc.description.abstractWe consider contraction of convex hypersurfaces by convex speeds, homogeneous of degree one in the principal curvatures, that are not necessarily smooth. We show how to approximate such a speed by a sequence of smooth speeds for which behaviour is well known. By obtaining speed and curvature pinching estimates for the flows by the approximating speeds, independent of the smoothing parameter, we may pass to the limit to deduce that the flow by the nonsmooth speed converges to a point in finite time that, under a suitable rescaling, is round in the C² sense, with the convergence being exponential.
dc.description.sponsorshipThe research of the second author was supported by an Australian Postgraduate Award. The research of the first, third, fourth and fifth authors was supported by Discovery Project grant DP120100097 of the Australian Research Council.en_AU
dc.format22 pages
dc.identifier.issn1435-5345
dc.identifier.urihttp://hdl.handle.net/1885/12321
dc.publisherDe Gruyter
dc.relationhttp://purl.org/au-research/grants/arc/DP120100097
dc.rights© De Gruyter 2014
dc.sourceJournal für die reine und angewandte Mathematik (2014)
dc.subjectcurvature
dc.subjectcontraction
dc.subjectconvex hypersurfaces
dc.subjectnonsmooth speeds
dc.subjectconvex speeds
dc.subjectsmooth speeds
dc.titleCurvature contraction of convex hypersurfaces by nonsmooth speeds
dc.typeJournal article
dcterms.dateAccepted2014-06-27
local.bibliographicCitation.issue2014
local.bibliographicCitation.lastpage22
local.bibliographicCitation.startpage1
local.contributor.affiliationAndrews, Benjamin Hardwick, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National Universityen_AU
local.contributor.authoruidu8610103en_AU
local.description.embargo2015-09-26
local.identifier.absfor010110 - Partial Differential Equations
local.identifier.absfor010102 - Algebraic and Differential Geometry
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
local.identifier.ariespublicationu8610103xPUB4
local.identifier.citationvolumeOnline Early Version
local.identifier.doi10.1515/crelle-2014-0087
local.identifier.scopusID2-s2.0-84879507926
local.identifier.thomsonID000320884800008
local.publisher.urlhttp://www.degruyter.com/en_AU
local.type.statusPublished Versionen_AU

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