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

Mao, Jing

69 ( 1 )  , pp.1 - 9 , 2015-06-09 , Faculty of Mathematics, Kyushu University
ISSN:1340-6116
NCID:AA10994346
Description
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 θ of the initial spacelike submanifold M_0 satisfies max_M0 cosh θ> √<2>.

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