A locally constrained mean curvature type flow with free boundary in a hyperbolic ball

Qiang, Tao; Weng, Liangjun; Xia, Chao

doi:10.1090/proc/15917

A locally constrained mean curvature type flow with free boundary in a hyperbolic ball
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by Tao Qiang, Liangjun Weng and Chao Xia;

Proc. Amer. Math. Soc. 151 (2023), 2641-2653

DOI: https://doi.org/10.1090/proc/15917

Published electronically: March 14, 2023

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Abstract:

In this paper, we study a locally constrained mean curvature flow with free boundary in a hyperbolic ball. Under the flow, the enclosed volume is preserved and the area is decreasing. We prove the long time existence and smooth convergence for such flow under certain star-shaped condition. As an application, we give a flow proof of the isoperimetric problem for the star-shaped free boundary hypersurfaces in a hyperbolic ball.

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