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2020 A sixth order flow of plane curves with boundary conditions
James McCoy, Glen Wheeler, Yuhan Wu
Tohoku Math. J. (2) 72(3): 379-393 (2020). DOI: 10.2748/tmj/1601085621

Abstract

For small-energy initial regular planar curves with generalised Neumann boundary conditions, we consider the steepest-descent gradient flow for the $L^2$-norm of the derivative of curvature with respect to arc length. We show that such curves between parallel lines converge exponentially in the $C^\infty$ topology in infinite time to straight lines.

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James McCoy. Glen Wheeler. Yuhan Wu. "A sixth order flow of plane curves with boundary conditions." Tohoku Math. J. (2) 72 (3) 379 - 393, 2020. https://doi.org/10.2748/tmj/1601085621

Information

Published: 2020
First available in Project Euclid: 26 September 2020

MathSciNet: MR4154824
Digital Object Identifier: 10.2748/tmj/1601085621

Subjects:
Primary: 53C44

Rights: Copyright © 2020 Tohoku University

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Vol.72 • No. 3 • 2020
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