Urbas, John2015-12-130075-4102http://hdl.handle.net/1885/76488We derive local integral estimates and monotonicity formulae for certain curvature quantities related to hypersurfaces of prescribed k-th mean curvature. We use these to improve interior curvature bounds established in previous work, and to derive a local Hölder gradient estimate for admissible solutions of the equation of prescribed scalar curvature.20032015-12-11