A survey on Inverse mean curvature flow in ROSSes

Abstract

In this survey we discuss the evolution by inverse mean curvature flow of star-shaped mean convex hypersurfaces in non-compact rank one symmetric spaces. We show similarities and differences between the case considered, with particular attention to how the geometry of the ambient manifolds influences the behaviour of the evolution. Moreover we try, when possible, to give an unified approach to the results present in literature.

Keywords

• inverse mean curvature flow
• sub-riemannian geometry
• webster curvature
• qc curvature
• 53c17
• 53c40
• 53c44