DARBOUXEQUATIONS AND ISOMETRIC EMBEDDING OF RIEMANNIAN MANIFOLDS WITHNONNEGATIVE CURVATURE INR

The present paper is concerned with the existence of golbal smooth solutions for the homogeneous Dirichlet boundary value problem of the Darboux equation and the case degenerate onthe boundary is contained As some applications the smooth isometric embeddings of positivelyand nonnegatively curved disks into R~3 are constructed.