Inverse curvature flows in hyperbolic space. (English) Zbl 1252.53078

Gerhardt, Claus

J. Differ. Geom. 89, No. 3, 487-527 (2011).

In the paper under review the author studies inverse curvature flows in hyperbolic space \({\mathbb H}^{n+1}\), \(n\geq 2\), with star-shaped initial hypersurfaces. He proves that the flows exist for all time and that leaves converge to infinity, become strongly convex exponentially fast and also more and more totally umbilic. After an appropriate rescaling the leaves converge in \(C^\infty\) to a sphere. The similar results in Euclidean space was proved in [C. Gerhardt, J. Differ. Geom. 32, No. 1, 299–314 (1990; Zbl 0708.53045)].

Reviewer: Sergei Platonov (Petrozavodsk)

MSC:

53C44

Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)

Keywords:

inverse curvature flow; hyperbolic space

Citations:

Zbl 0708.53045