Curvature flow of complete hypersurfaces in hyperbolic space

TL;DR

This paper investigates the evolution of complete hypersurfaces in hyperbolic space under curvature flow, focusing on boundary conditions at infinity, and establishes key estimates for the flow's behavior.

Contribution

It provides new a priori gradient and second derivative estimates for hypersurfaces evolving under curvature flow in hyperbolic space.

Findings

Established global gradient estimates.

Derived C^2 estimates for hypersurfaces.

Analyzed asymptotic boundary conditions at infinity.

Abstract

In this paper we continue our study of finding the curvature flow of complete hypersurfaces in hyperbolic space with a prescribed asymptotic boundary at infinity. Our main results are proved by deriving a priori global gradient estimates and C^2 estimates.