Evolution of radial graphs in hyperbolic space by their mean curvature

摘要

We consider the evolution of a surface F : M~n |→ H~(n+1) in hyperbolic space by mean curvature flow. That is, we study the one parameter family F_t = F(., t) of immersions with corresponding images M_t = F_t(M~n) such that (partial deriv)/((partial deriv)t)F(p, t) = H(p, t), p ∈ M~n F(p, 0) = F_0(p) where H(p, t) is the mean curvature vector of the hypersurface M_t at F(p, t) in hyperbolic space.