Curvature flow of complete convex hypersurfaces in hyperbolic space

TL;DR

This paper studies the evolution of convex hypersurfaces in hyperbolic space under a curvature flow, focusing on existence, convergence, and uniqueness with specified boundary conditions.

Contribution

It introduces a modified curvature flow approach for convex hypersurfaces in hyperbolic space, addressing boundary behavior and establishing key properties.

Findings

Proved existence of the flow under certain conditions

Established convergence to a unique limit hypersurface

Analyzed boundary asymptotics of the flow

Abstract

We investigate the existence, convergence and uniqueness of modified general curvature flow of convex hypersurfaces in hyperbolic space with a prescribed asymptotic boundary.