Long time behavior of Riemannian mean curvature flow of graphs

In this paper we consider long time behavior of a mean curvature flow of nonparametric surface in Rn, with respect to a conformal Riemannian metric. We impose zero boundary value, and we prove that the solution tends to 0 exponentially fast as t → ∞. Its normalization u/sup u tends to the first eigenfunction of the associated linearized problem.  2002 Elsevier Science (USA). All rights reserved.