Let $ f : \sum_1 \to \sum_2$ be a map between compact Riemannian manifolds of constant curvature. This article considers the evolution of the graph of f in $\sum_1 \times \sum_2$2 by the mean curvature flow. Under suitable conditions on the curvature of $\sum_1$ and $\sum_2$ 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 $f_t$ and $f_t$ converges to a constant map as $t$ approaches infinity. This also provides a regularity estimate for Lipschtz initial data.

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Let$X$be a complex manifold and let$f$:$X$→ℂ^{$p$}be a holomorphic mapping defining a complete intersection. We prove that the iterated Mellin transform of the residue integral associated with$f$has an analytic continuation to a neighborhood of the origin in ℂ^{$p$}.