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Closed ideal planar curves

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dc.contributor.authorAndrews, Ben
dc.contributor.authorMcCoy, James
dc.contributor.authorWheeler, Glen
dc.contributor.authorWheeler, Valentina-Mira
dc.date.accessioned2023-02-28T03:47:05Z
dc.date.issued2020
dc.date.updated2021-12-26T07:17:53Z
dc.description.abstractWe use a gradient flow to deform closed planar curves to curves with least variation of geodesic curvature in the L2 sense. Given a smooth initial curve we show that the solution to the flow exists for all time and, provided the length of the evolving curve remains bounded, smoothly converges to a multiply covered circle. Moreover, we show that curves in any homotopy class with initially small L3∥ks∥∥22 enjoy a uniform length bound under the flow, yielding the convergence result in these cases.en_AU
dc.format.mimetypeapplication/pdfen_AU
dc.identifier.issn1465-3060en_AU
dc.identifier.urihttp://hdl.handle.net/1885/286527
dc.language.isoen_AUen_AU
dc.provenancehttps://v2.sherpa.ac.uk/id/publication/25875/...."The accepted version can be archived in an institutional repository. 12 months embargo" from SHERPA/RoMEO site (as at 26/08/2020)
dc.publisherUniversity of Warwicken_AU
dc.relationhttp://purl.org/au-research/grants/arc/DP150100375en_AU
dc.rights© 2020 The authorsen_AU
dc.sourceGeometry and Topologyen_AU
dc.subjectconstant mean curvatureen_AU
dc.subjectcurvature flowen_AU
dc.subjectgeometric evolution equationen_AU
dc.titleClosed ideal planar curvesen_AU
dc.typeJournal articleen_AU
dcterms.accessRightsOpen Access
local.bibliographicCitation.issue2en_AU
local.bibliographicCitation.lastpage1049en_AU
local.bibliographicCitation.startpage1019en_AU
local.contributor.affiliationAndrews, Ben, College of Science, ANUen_AU
local.contributor.affiliationMcCoy, James , University of Newcastleen_AU
local.contributor.affiliationWheeler, Glen, University of Wollongongen_AU
local.contributor.affiliationWheeler, Valentina-Mira , University of Wollongongen_AU
local.contributor.authoruidAndrews, Ben, u8610103en_AU
local.description.notesImported from ARIESen_AU
local.identifier.absfor490402 - Algebraic and differential geometryen_AU
local.identifier.absfor490410 - Partial differential equationsen_AU
local.identifier.absseo280118 - Expanding knowledge in the mathematical sciencesen_AU
local.identifier.ariespublicationa383154xPUB13941en_AU
local.identifier.citationvolume24en_AU
local.identifier.doi10.2140/gt.2020.24.1019en_AU
local.identifier.scopusID2-s2.0-85092247476
local.publisher.urlhttps://msp.org/en_AU
local.type.statusAccepted Versionen_AU

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