Non-scale-invariant inverse curvature flows in hyperbolic space

TL;DR

This paper studies inverse curvature flows in hyperbolic space, showing that solutions starting from starshaped hypersurfaces exist indefinitely and tend to spherical shapes after rescaling.

Contribution

It introduces a new analysis of inverse curvature flows driven by positive powers of curvature functions in hyperbolic space, demonstrating long-term existence and convergence to spheres.

Findings

Solutions exist for all time

Rescaled solutions converge to spheres

Flow behavior depends on curvature function properties

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.