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<p>In this paper we prove two backward uniqueness theorems for extrinsic geometric flow of possibly non-compact hypersurfaces in general ambient complete Riemannian manifolds. These are applicable to a wide range of extrinsic geometric flow, including the mean curvature flow, inverse mean curvature flow, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="526_2025_3078_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> </InlineEquation>-Gauss curvature flow, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="526_2025_3078_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sigma _k\)</EquationSource> </InlineEquation> flow and so on.</p>

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Backward uniqueness of extrinsic geometric flows in general ambient manifolds

  • 期刊论文

  • 发表日期：

    2025年8月31日

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  • Dasong Li,
  • John Man Shun Ma

摘要

In this paper we prove two backward uniqueness theorems for extrinsic geometric flow of possibly non-compact hypersurfaces in general ambient complete Riemannian manifolds. These are applicable to a wide range of extrinsic geometric flow, including the mean curvature flow, inverse mean curvature flow, \(\alpha \) -Gauss curvature flow, \(\sigma _k\) flow and so on.