Inverse mean curvature flow with a free boundary in hyperbolic space
Xiaoxiang Chai (KIAS)
TL;DR
This paper investigates the inverse mean curvature flow with free boundary conditions in hyperbolic space, demonstrating convergence to a geodesic disk and establishing a related geometric inequality.
Contribution
It introduces a new analysis of inverse mean curvature flow with free boundary in hyperbolic space and proves convergence to a geodesic disk.
Findings
Flow converges to a totally geodesic disk in finite time
Establishes a Willmore type inequality in hyperbolic space
Applicable to convex hypersurfaces inside geodesic balls
Abstract
We study inverse mean curvature flow with 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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