On an area-preserving inverse curvature flow for plane curves

Zezhen Sun; Yuting Wu

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arXiv · 2507.22366

On an area-preserving inverse curvature flow for plane curves

Zezhen Sun·Yuting Wu

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Abstract

In this paper, we study a $1/\kappa^{n}$-type area-preserving non-local flow of convex closed plane curves for any $n>0$. We show that the flow exists globally, the length of evolving curve is non-increasing, and the limiting curve will be a circle in the $C^{\infty}$ metric as time $t\to\infty$.

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Zezhen Sun, Yuting Wu. 2025-07-30. On an area-preserving inverse curvature flow for plane curves. https://arxiv.org/abs/2507.22366

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