An interior curvature bound for hypersurfaces of prescribed $k$-th mean curvature

Abstract

We derive an interior curvature bound for k-admissible hypersurfaces in ℝn+1 of prescribed k-th mean curvature in terms of the Lp norm of the mean curvature for some p > kn/2. Examples show that in the cases k ≧ 3 such a bound is generally false if p