Non-parametric inverse curvature flows in the AdS-Schwarzschild manifold

TL;DR

This paper studies inverse curvature flows in the anti-de Sitter-Schwarzschild space, proving long-term existence and exponential convergence of the hypersurface's curvatures to a constant.

Contribution

It establishes the global existence and exponential convergence of inverse curvature flows in the AdS-Schwarzschild manifold with star-shaped initial data.

Findings

Solutions exist for all time

Principal curvatures converge exponentially to 1

Flow behavior in AdS-Schwarzschild space analyzed

Abstract

We consider the inverse curvature flows in the anti-de Sitter-Schwarzschild manifold with star-shaped initial hypersurface, driven by the 1-homogeneous curvature function. We show that the solutions exist for all time and the principle curvatures of the hypersurface converges to 1 exponentially fast.