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<p>In this paper, we study a curve flow which preserves the anisotropic length of the evolving curve, and show that for any convex closed initial curve, the flow exists for all time and the evolving curve converges to a homothety of the boundary of some Wulff shape defined by anisotropic function as time <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2131_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(t\rightarrow \infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>t</mi> <mo stretchy="false">→</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Deforming Convex Curves with Constant Anisotropic Length

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Zezhen Sun

摘要

In this paper, we study a curve flow which preserves the anisotropic length of the evolving curve, and show that for any convex closed initial curve, the flow exists for all time and the evolving curve converges to a homothety of the boundary of some Wulff shape defined by anisotropic function as time \(t\rightarrow \infty \) t → ∞ .