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<p>In this paper, we give a unified definition on hypersurfaces with constant mean curvature in Finsler manifolds by volume-preserving variation. Then we derive the correspondence on the mean curvatures of hypersurfaces for homothetic navigation. Finally, we deduce a Heintze–Karcher type inequality and prove an Alexandrov type theorem in special Finsler spaces.</p>

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On Hypersurfaces with Constant Mean Curvature in Finsler Manifolds

  • 期刊论文

  • 发表日期：

    2025年4月5日

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  • Yali Chen,
  • Qun He,
  • Yantong Qian

摘要

In this paper, we give a unified definition on hypersurfaces with constant mean curvature in Finsler manifolds by volume-preserving variation. Then we derive the correspondence on the mean curvatures of hypersurfaces for homothetic navigation. Finally, we deduce a Heintze–Karcher type inequality and prove an Alexandrov type theorem in special Finsler spaces.