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Inverse Gauss curvature flow with free boundary
2019-05-24 09:28:55

We consider strictly convex hypersurfaces with boundary which meet a strictlyconvex cone perpendicularly. If those hypersurfaces expand inside this cone by thepower of the Gauss curvature, we prove that this evolution exists for all the timeand the evolving hypersurfaces converge smoothly to a piece of round sphere afterrescaling.