Inverse Mean Curvature Flow for Star-Shaped Hypersurfaces Evolving in a Cone

Marquardt, Thomas

doi:10.1007/s12220-011-9288-7

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Inverse Mean Curvature Flow for Star-Shaped Hypersurfaces Evolving in a Cone

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Marquardt, Thomas
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Marquardt, T. (2013). Inverse Mean Curvature Flow for Star-Shaped Hypersurfaces Evolving in a Cone. Journal of Geometric Analysis, 23(3), 1303-1313. doi:10.1007/s12220-011-9288-7.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0015-14AE-A

Abstract

For a given convex cone we consider hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicular. The evolution of those hypersurfaces inside the cone yields a nonlinear parabolic Neumann problem. We show that one can use the convexity of the cone to prove long time existence of this flow. Finally, we show that the hypersurfaces converge smoothly to a piece of the round sphere.