Mean Curvature Ow of Graphs in Σ1 × Σ2

Abstract

" Let Σ_1 and Σ_2 be m and n dimensional Riemannian manifolds of constant curvature respectively. We assume that w is a unit constant m-form in Σ_1 with respect to which Σ_0 is a graph. We set v = \\frac{\\sqrt{p}}{2} for all x, then the mean curvature flow has a global solution F under some suitable conditions on the curvatrue of Σ_1 and Σ_2."