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Pinching estimates and motion of hypersurfaces by curvature functions

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Andrews, Benjamin

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Second derivative pinching estimates are proved for a class of parabolic equations, including motion of hypersurfaces by curvature functions such as quotients of elementary symmetric functions of curvature. The estimates imply convergence of convex hypersurfaces to spheres under these flows, improving earlier results of B. Chow and the author. The result is obtained via a detailed analysis of gradient terms in the equations satisfied by second derivatives.

dc.contributor.authorAndrews, Benjamin
dc.date.accessioned2015-12-08T22:23:49Z
dc.identifier.issn0075-4102
dc.identifier.urihttp://hdl.handle.net/1885/33027
dc.description.abstractSecond derivative pinching estimates are proved for a class of parabolic equations, including motion of hypersurfaces by curvature functions such as quotients of elementary symmetric functions of curvature. The estimates imply convergence of convex hypersurfaces to spheres under these flows, improving earlier results of B. Chow and the author. The result is obtained via a detailed analysis of gradient terms in the equations satisfied by second derivatives.
dc.publisherWalter de Gruyter
dc.sourceJournal fur Reine und Angewandte Mathematik
dc.titlePinching estimates and motion of hypersurfaces by curvature functions
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume608
dc.date.issued2007
local.identifier.absfor010112 - Topology
local.identifier.ariespublicationu3169606xPUB98
local.type.statusPublished Version
local.contributor.affiliationAndrews, Benjamin, College of Physical and Mathematical Sciences, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.startpage17
local.bibliographicCitation.lastpage33
local.identifier.doi10.1515/CRELLE.2007.051
dc.date.updated2015-12-08T08:55:18Z
local.identifier.scopusID2-s2.0-34547678250
CollectionsANU Research Publications

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