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

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.

22 pages. Some revisions have been made to v2

References in corpus (2)

• Inverse curvature flow in anti-de Sitter-Schwarzschild manifold
• Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds

Cited by in corpus (9)

• Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature
• Inverse curvature flows in Riemannian warped products
• Minimal hypersurfaces and boundary behavior of compact manifolds with nonnegative scalar curvature
• Inverse mean curvature flows in warped product manifolds
• Inverse curvature flow in anti-de Sitter-Schwarzschild manifold
• Inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space ${\mathbb{R}}_1^{n+1}$
• A class of inverse curvature flows for star-shaped hypersurfaces evolving in a cone
• Inverse Gauss curvature flow in a time cone of Lorentz-Minkowski space ${\mathbb{R}}_1^{n+1}$
• Inverse Gauss curvature flows with free boundaries in a cone