- Title
- Closed ideal planar curves
- Creator
- Andrews, Ben; McCoy, James; Wheeler, Glen; Wheeler, Valentina-Mira
- Relation
- ARC.DP150100375 http://purl.org/au-research/grants/arc/DP150100375
- Relation
- Geometry & Topology Vol. 24, Issue 2, p. 1019-1049
- Publisher Link
- http://dx.doi.org/10.2140/gt.2020.24.1019
- Publisher
- Mathematical Sciences Publishers
- Resource Type
- journal article
- Date
- 2020
- Description
- In this paper we 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 multiplycovered circle. Moreover, we show that curves in any homotopy class with initially small L³‖k₈‖²₂ enjoy a uniform length bound under the flow, yielding the convergence result in these cases.
- Subject
- gradient flow; planar curves; curves; multiply-covered circle
- Identifier
- http://hdl.handle.net/1959.13/1445349
- Identifier
- uon:42568
- Identifier
- ISSN:1465-3060
- Language
- eng
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