Inverse mean curvature flow in complex hyperbolic space
Differential Geometry
2018-03-29 v4
Abstract
We consider the evolution by inverse mean curvature flow of a closed, mean convex and star-shaped hypersurface in the complex hyperbolic space. We prove that the flow is defined for any positive time, the evolving hypersurface stays star-shaped and mean convex. Moreover the induced metric converges, after rescaling, to a conformal multiple of the standard sub- Riemannian metric on the sphere. Finally we show that there exists a family of examples such that the Webster curvature of this sub-Riemannian limit is not constant.
Cite
@article{arxiv.1610.01886,
title = {Inverse mean curvature flow in complex hyperbolic space},
author = {Giuseppe Pipoli},
journal= {arXiv preprint arXiv:1610.01886},
year = {2018}
}
Comments
31 pages, minor changes. This is the final version to appear on Annales scientifiques de l'ENS