THE MAXIMUM PRINCIPLE FOR HYPERSURFACES WITH VANISHING CURVATURE FUNCTIONS

We extend the maximum principle, known for hypersurfaces of a Euclidea n (n + 1)-space R(n+1) with positive constant curvature function sigma (k) = c > 0, to a generic class of hypersurfaces with vanishing curvat ure sigma(k) = 0, 1 less than or equal to k < n. Using the Alexandrov reflection method, this result can be extended to hypersurfaces with v anishing curvature function having certain symmetry and uniqueness pro perties that were known for minimal surfaces.