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Inverse mean curvature flow in complex hyperbolic space
- Publication Year :
- 2016
-
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.<br />Comment: 31 pages, minor changes. This is the final version to appear on Annales scientifiques de l'ENS
- Subjects :
- Mathematics - Differential Geometry
53C17, 53C40, 53C44
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1610.01886
- Document Type :
- Working Paper