Some Integral Formulas for the (r + 1)th Mean Curvature of a Closed Hypersurface

Abstract

By using the operator 𝐿𝑟, we define the notions of rth order and rth type of a Euclidean hypersurface. By the use of these notions, we are able to obtain some sharp estimates of the (𝑟+1)th mean curvature for a closed hypersurface of the Euclidean space in terms of rth order.