A NEW WAY TO DIRICHLET PROBLEMS FOR MINIMAL SURFACE SYSTEMS IN ARBITRARY DIMENSIONS AND CODIMENSIONS

摘要

In this paper, by considering a special case of the spacelike mean curvature flow investigated by Li and Salavessa [Math. Z. 269 (2011), 697-719], we obtain a condition for the existence of smooth solutions of the Dirichlet problem for the minimal surface equation in arbitrary codimension. We also show that our condition is sharper than Wang's [Comm Pure Appl. Math. 57 (2004), 267-281] provided that the hyperbolic angle 9 of the initial spacelike submanifold M-0 satisfies max(M0) cosh theta > root 2.