Pinching and asymptotical roundness for inverse curvature flows in Euclidean space

Abstract

We consider inverse curvature flows in the $(n+1)$-dimensional Euclidean space, $n\ge 2,$ expanding by arbitrary negative powers of a 1-homogeneous, monotone curvature function $F$ with some concavity properties. We obtain asymptotical roundness, meaning that circumradius minus inradius of the flow hypersurfaces decays to zero and that the flow becomes close to a flow of spheres.

13 pages. In this final version we were able to remove the dimension restrictions which had to be imposed in the former versions. Comments, discussions or suggestions are welcome

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