We prove gradient estimates for hypersurfaces in the hyperbolic space Hn+1, expanding by negative powers of a certain class of homogeneous curvature functions F. We obtain optimal gradient estimates for hypersurfaces evolving by certain powers p > 1 of F-1 and smooth convergence of the properly rescaled hypersurfaces. In particular, the full convergence result holds for the inverse Gauss curvature flow of surfaces without any further pinching condition besides convexity of the initial hypersurface.
@article{bwmeta1.element.doi-10_1515_geofl-2015-0002,
author = {Julian Scheuer},
title = {Gradient estimates for inverse curvature flows in hyperbolic space},
journal = {Geometric Flows},
volume = {1},
year = {2015},
zbl = {1317.53089},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_geofl-2015-0002}
}
Julian Scheuer. Gradient estimates for inverse curvature flows in hyperbolic space. Geometric Flows, Tome 1 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_geofl-2015-0002/
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