Non-scale-invariant inverse curvature flows in hyperbolic space

Abstract

We consider inverse curvature flows in hyperbolic space with starshaped initial hypersurface, driven by positive powers of a homogeneous curvature function. The solutions exist for all time and, after rescaling, converge to a sphere.

The rescaling, under which the flow hypersurfaces converge to a constant, had to be modified due to a mistake in the corresponding proof in the first version. Several typing errors were corrected

Cited by in corpus (11)

• Locally constrained inverse curvature flows
• The inverse mean curvature flow in warped cylinders of non-positive radial curvature
• The inverse mean curvature flow perpendicular to the sphere
• New pinching estimates for Inverse curvature flows in space forms
• Surfaces expanding by non-concave curvature functions
• Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature
• Non-parametric inverse curvature flows in the AdS-Schwarzschild manifold
• Inverse curvature flows in Riemannian warped products
• The Minkowski inequality in de Sitter space
• Gradient estimates for inverse curvature flows in hyperbolic space
• Shifted inverse curvature flows in hyperbolic space