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<p>In this paper, we study a mean curvature type flow with capillary boundary in a horoball in hyperbolic space. Our flow preserves the volume of the bounded domain enclosed by the hypersurface and monotonically decreases the energy functional. We show that it has the long time existence and converges to a truncated umbilical hypersurface which could be geodesic sphere, totally geodesic hyperplane, horosphere or equidistant hypersurface. As an application, we solve an isoperimetric type problem for hypersurfaces with capillary boundary in a horoball.</p>

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A Mean Curvature Type Flow with Capillary Boundary in a Horoball in Hyperbolic Space

  • 期刊论文

  • 发表日期：

    2025年3月20日

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  • Jinyu Guo

摘要

In this paper, we study a mean curvature type flow with capillary boundary in a horoball in hyperbolic space. Our flow preserves the volume of the bounded domain enclosed by the hypersurface and monotonically decreases the energy functional. We show that it has the long time existence and converges to a truncated umbilical hypersurface which could be geodesic sphere, totally geodesic hyperplane, horosphere or equidistant hypersurface. As an application, we solve an isoperimetric type problem for hypersurfaces with capillary boundary in a horoball.