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<p>In this paper we establish estimates for the area of capillary stable minimal hypersurfaces in a high dimensional Riemannian manifold <i>M</i> and the area of their boundaries, in terms of the scalar curvature of <i>M</i> and the mean curvature of the boundary <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_1998_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(\partial M\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>∂</mi> <mi>M</mi> </mrow> </math></EquationSource> </InlineEquation>. Next, we prove rigidity results for the geometry of <i>M</i> when equalities are attained. Lastly, we explore the relationship between the positive scalar curvature of the Riemannian manifold and the topological invariants of the capillary stable minimal hypersurface in an <i>n</i>-dimensional Riemannian manifold.</p>

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Capillary Stable Minimal Hypersurfaces in a High Dimensional Riemannian Manifold

  • 期刊论文

  • 发表日期：

    2025年4月2日

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  • Sanghun Lee,
  • Sangwoo Park,
  • Juncheol Pyo

摘要

In this paper we establish estimates for the area of capillary stable minimal hypersurfaces in a high dimensional Riemannian manifold M and the area of their boundaries, in terms of the scalar curvature of M and the mean curvature of the boundary \(\partial M\) ∂ M . Next, we prove rigidity results for the geometry of M when equalities are attained. Lastly, we explore the relationship between the positive scalar curvature of the Riemannian manifold and the topological invariants of the capillary stable minimal hypersurface in an n-dimensional Riemannian manifold.