Inverse mean curvature flow in complex hyperbolic space

Giuseppe Pipoli

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arXiv · 1610.01886

Inverse mean curvature flow in complex hyperbolic space

Giuseppe Pipoli

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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.

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Giuseppe Pipoli. 2016-10-06. Inverse mean curvature flow in complex hyperbolic space. https://arxiv.org/abs/1610.01886

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