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arXiv · 1708.04827

Evolution of Locally Convex Closed Curves in Nonlocal Curvature Flows

Natasa Sesum·Dong-Ho Tsai·Xiao-Liu Wang
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Abstract

We provide sufficient conditions on an initial curve for the area preserving and the length preserving curvature flows of curves in a plane, to develop a singularity at some finite time or converge to an $m$-fold circle as time goes to infinity. For the area-preserving flow, the positivity of the enclosed algebraic area determines whether the curvature blows up in finite time or not, while for the length-preserving flow, it is the positivity of an energy associated with initial curve that plays such a role.

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Natasa Sesum, Dong-Ho Tsai, Xiao-Liu Wang. 2017-08-16. Evolution of Locally Convex Closed Curves in Nonlocal Curvature Flows. https://arxiv.org/abs/1708.04827

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