We study the inverse mean curvature flow with a free boundary supported on geodesic spheres in hyperbolic space. Starting from any convex hypersurface inside a geodesic ball with a free boundary, the flow converges to a totally geodesic disk in finite time. Using the convergence result, we show a Willmore type inequality.

中文翻译：

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双曲空间中具有自由边界的反平均曲率流

我们研究双曲空间中测地球体支持的自由边界的逆平均曲率流。从具有自由边界的测地线球内的任何凸超曲面开始，流动在有限时间内收敛到完全测地线圆盘。利用收敛结果，我们展示了威尔莫尔型不等式。