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arXiv · 1408.1805

On Area-preserving and Length-preserving Nonlocal Flow of Convex Closed Plane Curves

Dong-Ho Tsai·Xiao-Liu Wang
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Abstract

For any $\alpha>0,$ we study $k^{\alpha}$-type length-preserving and area-preserving nonlocal flow of convex closed plane curves and show that these two types of flow evolve such curves into round circles in $C^{\infty}% $-norm.$\ $Other relevant $k^{\alpha}$-type nonlocal flow is also discussed when $\alpha\geq1.\ $

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Dong-Ho Tsai, Xiao-Liu Wang. 2014-08-08. On Area-preserving and Length-preserving Nonlocal Flow of Convex Closed Plane Curves. https://doi.org/10.1007/s00526-015-0915-1

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