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<p>For <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, we construct <i>I</i>-dimensional family of embedded ancient solutions to mean curvature flow emerging from an unstable minimal hypersurface <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Σ</mi> </math></EquationSource> </InlineEquation> with finite total curvature in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {R}^{n+1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>, where <i>I</i> is the Morse index of the Jacobi operator on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\Sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Σ</mi> </math></EquationSource> </InlineEquation>.</p>

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Ancient mean curvature flows from minimal hypersurfaces

  • 期刊论文

  • 发表日期：

    2026年2月10日

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  • Yongheng Han

摘要

For \(n\ge 2\) n ≥ 2 , we construct I-dimensional family of embedded ancient solutions to mean curvature flow emerging from an unstable minimal hypersurface \(\Sigma \) Σ with finite total curvature in \(\mathbb {R}^{n+1}\) R n + 1 , where I is the Morse index of the Jacobi operator on \(\Sigma \) Σ .