A class of inverse quotient curvature flow in the AdS-Schwarzschild manifold

Abstract

In this paper, we study the asymptotic behavior of a class of inverse quotient curvature flow in the anti-de Sitter-Schwarzschild manifold. We prove that under suitable convex conditions for the initial hypersurface, one can get the long-time existence for the inverse curvature flow. Moreover, we also get that the principal curvatures of the evolving hypersurface converge to 1 when t → +∞.