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

Hyunsuk Kang, Lami Kim, Ki-Ahm Lee

Published 2013-08-20, updated 2019-10-10Version 3

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.