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dc.contributor.authorColding, Tobias
dc.contributor.authorMinicozzi, William
dc.contributor.authorWhite, Brian
dc.contributor.authorIlmanen, Tom
dc.date.accessioned2015-01-22T20:41:53Z
dc.date.available2015-01-22T20:41:53Z
dc.date.issued2013-07
dc.date.submitted2012-05
dc.identifier.issn0022-040X
dc.identifier.issn1945-743X
dc.identifier.urihttp://hdl.handle.net/1721.1/93156
dc.description.abstractThe entropy of a hypersurface is a geometric invariant that measures complexity and is invariant under rigid motions and dilations. It is given by the supremum over all Gaussian integrals with varying centers and scales. It is monotone under mean curvature flow, thus giving a Lyapunov functional. Therefore, the entropy of the initial hypersurface bounds the entropy at all future singularities. We show here that not only does the round sphere have the lowest entropy of any closed singularity, but there is a gap to the second lowest.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Grant DMS 11040934)en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Grant DMS 0906233)en_US
dc.description.sponsorshipNational Science Foundation (U.S.). Focused Research Group (Grant DMS 0854774)en_US
dc.description.sponsorshipNational Science Foundation (U.S.). Focused Research Group (Grant DMS 0853501)en_US
dc.language.isoen_US
dc.publisherInternational Press of Boston, Inc.en_US
dc.relation.isversionofhttp://projecteuclid.org/euclid.jdg/1375124609en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleThe Round Sphere Minimizes Entropy among Closed Self-Shrinkersen_US
dc.typeArticleen_US
dc.identifier.citationColding, Tobias Holck, Tom Ilmanen, William P. Minicozzi, and Brian White. "The Round Sphere Minimizes Entropy Among Closed Self-Shrinkers." J. Differential Geom. 95.1 (2013): 53-69.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorColding, Tobiasen_US
dc.contributor.mitauthorMinicozzi, Williamen_US
dc.relation.journalJournal of Differential Geometryen_US
dc.eprint.versionOriginal manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dspace.orderedauthorsColding, Tobias Holck; Ilmanen, Tom; Minicozzi, William P.; White, Brianen_US
dc.identifier.orcidhttps://orcid.org/0000-0001-6208-384X
dc.identifier.orcidhttps://orcid.org/0000-0003-4211-6354
mit.licenseOPEN_ACCESS_POLICYen_US


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