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<p>In any dimension <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n+1\ge 4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>≥</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation> we construct a sequence of closed <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((n+1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-dimensional Riemannian manifolds with positive Ricci curvature admitting embedded two-sided minimal hypersurfaces such that the following hold: (i) any such hypersurface has Morse index one; (ii) the first Betti numbers of the hypsersurfaces are not uniformly bounded along the sequence.</p>

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Ricci curvature and minimal hypersurfaces with large Betti numbers

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月7日

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  • Davi Maximo,
  • Philipp Reiser,
  • Daniele Semola

摘要

In any dimension \(n+1\ge 4\) n + 1 ≥ 4 we construct a sequence of closed \((n+1)\) ( n + 1 ) -dimensional Riemannian manifolds with positive Ricci curvature admitting embedded two-sided minimal hypersurfaces such that the following hold: (i) any such hypersurface has Morse index one; (ii) the first Betti numbers of the hypsersurfaces are not uniformly bounded along the sequence.