Long-time Existence and Convergence of Graphic Mean Curvature Flow in Arbitrary Codimension
نویسنده
چکیده
Let f : Σ1 7→ Σ2 be a map between compact Riemannian manifolds of constant curvature. This article considers the evolution of the graph of f in Σ1×Σ2 by the mean curvature flow. Under suitable conditions on the curvature of Σ1 and Σ2 and the differential of the initial map, we show that the flow exists smoothly for all time. At each instant t, the flow remains the graph of a map ft and ft converges to a constant map as t approaches infinity. This also provides a regularity estimate for Lipschtz initial data.
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