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arXiv · 1308.4347

Anisotropic flow of convex hypersurfaces by the square root of the scalar curvature

Hyunsuk Kang·Lami Kim·Ki-Ahm Lee
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Abstract

We show the existence of a smooth solution for the flow deformed by the square root of the scalar curvature multiplied by a positive anisotropic factor $\psi$ given a strictly convex initial hypersurface in Euclidean space suitably pinched. We also prove the convergence of rescaled surfaces to a smooth limit manifold which is a round sphere. In dimension two, it is shown that, with a volume preserving rescaling, the limit profile satisfies a soliton equation.

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Hyunsuk Kang, Lami Kim, Ki-Ahm Lee. 2013-08-20. Anisotropic flow of convex hypersurfaces by the square root of the scalar curvature. https://arxiv.org/abs/1308.4347

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