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<p>In this paper, we prove a Heintze-Karcher type inequality for capillary hypersurfaces supported on various hypersurfaces in hyperbolic space. The equality case occurs only for capillary hypersurfaces that are totally umbilical. Then we apply this result to prove the Alexandrov type theorem for embedded capillary hypersurfaces in the hyperbolic space. In addition, we prove some other rigidity results for capillary hypersurfaces supported on a totally geodesic plane in the hyperbolic space.</p>

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Some Rigidity Results on Compact Hypersurfaces with Capillary Boundary in the Hyperbolic Space

  • 期刊论文

  • 发表日期：

    2026年5月5日

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  • Yimin Chen,
  • Juncheol Pyo

摘要

In this paper, we prove a Heintze-Karcher type inequality for capillary hypersurfaces supported on various hypersurfaces in hyperbolic space. The equality case occurs only for capillary hypersurfaces that are totally umbilical. Then we apply this result to prove the Alexandrov type theorem for embedded capillary hypersurfaces in the hyperbolic space. In addition, we prove some other rigidity results for capillary hypersurfaces supported on a totally geodesic plane in the hyperbolic space.