Curvature Flow of Complete Convex Hypersurfaces in Hyperbolic Space

Abstract

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

Curvature flow of complete hypersurfaces in hyperbolic space

“…In order to prove a global existence for the Dirichlet problem (1.18), we first need a short time existence theorem. Here we shall apply Theorem 3.1 of [LX11] directly. For completeness let's restate the theorem as following:…”

“…Evolution equations for some geometric quantities. For the reader's convenience, we now compute the evolution equations for some affine geometric quantities that were first derived in [LX11]. In this section we shall write…”