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<p>In this paper, we investigate compact Riemannian manifolds with boundary satisfying V-static-type equation. By combining a generalized Reilly formula with Steklov-type boundary value problems, we derive new integral inequalities for geometric quantities associated with the boundary. These inequalities lead to rigidity results, including characterizations of geodesic balls in space forms. In particular, these results provide new insights into classical rigidity theorems.</p>

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Integral inequalities and rigidity for V-static-type equation on manifolds with boundary

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月23日

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  • Maria Andrade

摘要

In this paper, we investigate compact Riemannian manifolds with boundary satisfying V-static-type equation. By combining a generalized Reilly formula with Steklov-type boundary value problems, we derive new integral inequalities for geometric quantities associated with the boundary. These inequalities lead to rigidity results, including characterizations of geodesic balls in space forms. In particular, these results provide new insights into classical rigidity theorems.