Communications in Analysis and Geometry

Volume 11 (2003)

Number 4

Evolution of radial graphs in hyperbolic space by their mean curvature

Pages: 675 – 698

DOI: https://dx.doi.org/10.4310/CAG.2003.v11.n4.a2

Author

Philip Unterberger

Abstract

We consider the evolution of a surface F : Mⁿ ↦ ℋⁿ⁺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 (Mⁿ) such that

δ / δt F(p, t) =ℋ(p, t), p ∈ Mⁿ

F(p, 0) = F₀(p)

where ℋ(p, t) is the mean curvature vector of the hypersurface M_t at F(p, t) in hyperbolic space.

Published 1 January 2003