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<p>In this paper, we use inverse mean curvature flow to prove a sharp Minkowski-type inequality for compact, mean convex and star-shaped hypersurfaces in a class of non-positive constant scalar curvature warped product manifolds. This inequality generalizes the one for hypersurfaces in the Anti-de Sitter-Schwarzschild manifold proved in [4]. The proof relies on a monotonicity formula for inverse mean curvature flow and geometric inequalities.</p>

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A Minkowski-Type Inequality for Hypersurfaces in Warped Product Manifolds with Non-Positive Constant Scalar Curvature

  • 期刊论文

  • 发表日期：

    2026年7月6日

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  • Wei Chen,
  • Guanghan Li

摘要

In this paper, we use inverse mean curvature flow to prove a sharp Minkowski-type inequality for compact, mean convex and star-shaped hypersurfaces in a class of non-positive constant scalar curvature warped product manifolds. This inequality generalizes the one for hypersurfaces in the Anti-de Sitter-Schwarzschild manifold proved in [4]. The proof relies on a monotonicity formula for inverse mean curvature flow and geometric inequalities.