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<p>Given a complete Riemannian metric of nonnegative scalar curvature on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Sigma \times (-\infty , 0 ] \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Σ</mi> <mo>×</mo> <mo stretchy="false">(</mo> <mo>-</mo> <mi>∞</mi> <mo>,</mo> <mn>0</mn> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Σ</mi> </math></EquationSource> </InlineEquation> denotes a 2-sphere, we exhibit conditions that imply the existence of a closed minimal surface homologous to the boundary.</p>

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Horizons in noncompact fill-ins of nonnegative scalar curvature

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月24日

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  • Pengzi Miao,
  • Sehong Park

摘要

Given a complete Riemannian metric of nonnegative scalar curvature on \(\Sigma \times (-\infty , 0 ] \) Σ × ( - ∞ , 0 ] , where \(\Sigma \) Σ denotes a 2-sphere, we exhibit conditions that imply the existence of a closed minimal surface homologous to the boundary.