The Dirichlet problem for the equationdet || zy|| = <pizt....... z„, Z, x t, x } . Part I

When there are only two variables, the solution of (1.1), for / and h > 0, is invariably a convex surface. If there are a larger number of variables,

then this cannot be guaranteed because det | |^ j | | may be positive when its eigenvalues and, accordingly, the principal radii of curvature of the surface are of unlike signs, the only condition being negative signs must occur in pairs.