Abstract
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.
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Acknowledgements
Research of the author has been supported by KIAS Grants under the research code MG074402. The revision has been partially supported by National Research Foundation of Korea grant No. 2022R1C1C1013511. The author would also like to thank Yizi Wang (CUHK) for some useful discussions and Julian Scheuer (Cardiff) for pointing out some inaccuracies in an earlier version of the paper. The author would also like to thank the refree for various comments to improve the paper.
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Communicated by R. M. Schoen.
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