Inverse curvature flows in hyperbolic space

Claus Gerhardt

Inverse curvature flows in hyperbolic space

Differential Geometry 2014-06-06 v5 Analysis of PDEs

Authors: Claus Gerhardt

Abstract

We consider inverse curvature flows in $\Hh$ with star-shaped initial hypersurfaces and prove that the flows exist for all time, and that the leaves converge to infinity, become strongly convex exponentially fast and also more and more totally umbilic. After an appropriate rescaling the leaves converge in $C^\infty$ to a sphere.

Keywords

curvature flow mean curvature flow geodesic flow

Cite

@article{arxiv.1101.2578,
  title  = {Inverse curvature flows in hyperbolic space},
  author = {Claus Gerhardt},
  journal= {arXiv preprint arXiv:1101.2578},
  year   = {2014}
}

Comments

v5: Removed Lemma 6.12 which is false and corrected the claim that the rescaled functions in (1.12) converge to a constant; they converge to a smooth function

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