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AUTHOR Pyo, Juncheol
TITLE Rigidity of minimal hypersurfaces with free boundary in a ball
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JOURNAL GEOMETRIAE DEDICATA, 2022
ABSTRACT In this paper, we give two rigidity results of free boundary hypersurfaces in a ball. First, we prove that any minimal hypersurface with free boundary in a closed geodesic ball in a round open hemisphere S-+(n+1) which is Killing-graphical is a geodesic disk. We note that we do not assume any topological condition on the hypersurface. We consider analogous result for self-shrinkers of the mean curvature flow. More precisely, we proved that any graphical self-shrinker with free boundary in a ball centered at the origin in Rn+1 is a flat disk passing through the origin.
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