The existence of hypersurfaces of constant Gauss curvature with prescribed boundary.
The authors establish the existence of hypersurfaces of constant Gauss-Kronecker curvature with prescribed boundary. This is achieved by means of Monge-Ampere type equations. Important local properties of locally convex hypersurfaces with boundary are proven. A special attention is paid to the regularity of the constructed hypersurfaces.
scientific article; zbMATH DE number 2171918