Mixed volume preserving curvature flows in hyperbolic space
Differential Geometry
2012-08-10 v1 Analysis of PDEs
Abstract
We consider curvature flows in hyperbolic space with a monotone, symmetric, homogeneous of degree 1 curvature function F. Furthermore we assume F to be either concave and inverse concave or convex. For compact initial hypersurfaces, which are strictly convex by horospheres, we show the long time existence of mixed volume preserving curvature flows. Furthermore we show that these flows converge exponentially in the C-infinity topology to a geodesic sphere.
Cite
@article{arxiv.1208.1898,
title = {Mixed volume preserving curvature flows in hyperbolic space},
author = {Matthias Makowski},
journal= {arXiv preprint arXiv:1208.1898},
year = {2012}
}