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<p>We show that the Morse index of unstable closed minimal hypersurface <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Σ</mi> </math></EquationSource> </InlineEquation> in a compact semi-simple Riemannian symmetric space <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(M=G/K\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mo>=</mo> <mi>G</mi> <mo stretchy="false">/</mo> <mi>K</mi> </mrow> </math></EquationSource> </InlineEquation> is bounded from below by constant times the first Betti number of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\Sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Σ</mi> </math></EquationSource> </InlineEquation>. Our proof is based on a natural extension of the previous method and this also provides a novel approach for the index estimate.</p>

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Index estimate by first Betti number of minimal hypersurfaces in compact symmetric spaces

  • 期刊论文

  • 发表日期：

    2025年12月6日

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  • Toru Kajigaya,
  • Keita Kunikawa

摘要

We show that the Morse index of unstable closed minimal hypersurface \(\Sigma \) Σ in a compact semi-simple Riemannian symmetric space \(M=G/K\) M = G / K is bounded from below by constant times the first Betti number of \(\Sigma \) Σ . Our proof is based on a natural extension of the previous method and this also provides a novel approach for the index estimate.