The maximum principle for hypersurfaces with vanishing curvature functions (Q1891960)

We extend the maximum principle, known for hypersurfaces of Euclidean \((n+1)\)-space with positive constant curvature function \(\sigma_ k = c > 0\), to a generic class of hypersurfaces with vanishing curvature \(\sigma_ k = 0\), \(1 \leq k < n\). This allows the application of Alexandrov reflection method to this class of hypersurfaces, yielding certain symmetry and uniqueness properties that were known for minimal surfaces.