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Evolution of closed curves by length-constrained curve diffusion

Journal Article


Abstract


  • 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.

Publication Date


  • 2019

Citation


  • McCoy, J., Wheeler, G. & Wu, Y. (2019). Evolution of closed curves by length-constrained curve diffusion. Proceedings of the American Mathematical Society, 147 (8), 3493-3506.

Scopus Eid


  • 2-s2.0-85074216112

Number Of Pages


  • 13

Start Page


  • 3493

End Page


  • 3506

Volume


  • 147

Issue


  • 8

Place Of Publication


  • United States

Abstract


  • 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.

Publication Date


  • 2019

Citation


  • McCoy, J., Wheeler, G. & Wu, Y. (2019). Evolution of closed curves by length-constrained curve diffusion. Proceedings of the American Mathematical Society, 147 (8), 3493-3506.

Scopus Eid


  • 2-s2.0-85074216112

Number Of Pages


  • 13

Start Page


  • 3493

End Page


  • 3506

Volume


  • 147

Issue


  • 8

Place Of Publication


  • United States