Inverse mean curvature flow in complex hyperbolic space

2016/10/06 by Giuseppe Pipoli, Pipoli, Giuseppe
Mathematics · Physics and Astronomy · #53C17 #53C40 #53C44 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1610.01886

openalex publication_date 2016/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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