- Title
- Evolution of closed curves by length-constrained curve diffusion
- Creator
- McCoy, James; Wheeler, Glen; Wu, Yuhan
- Relation
- ARC.DP150100375 http://purl.org/au-research/grants/arc/DP150100375
- Relation
- Proceedings of the American Mathematical Society Vol. 147, Issue 8, p. 3493-3506
- Publisher Link
- http://dx.doi.org/10.1090/proc/14473
- Publisher
- American Mathematical Society
- Resource Type
- journal article
- Date
- 2019
- Description
- We show that any initial closed curve suitably close to a circle flows under length-constrained curve diffusion to a round circle in infinite time with exponential convergence. We provide an estimate on the total length of time for which such curves are not strictly convex. We further show that there are no closed translating solutions to the flow and that the only closed rotators are circles.
- Subject
- curvature flow; higher order quasilinear partial differential equation; curve diffusion row; differential geometry of plane curves
- Identifier
- http://hdl.handle.net/1959.13/1406992
- Identifier
- uon:35680
- Identifier
- ISSN:0002-9939
- Language
- eng
- Full Text
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| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
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