International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 784028, 15 pages
http://dx.doi.org/10.1155/2012/784028
Research Article

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

Akram Mohammadpouri and S. M. B. Kashani

Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, Iran

Received 24 April 2012; Accepted 27 June 2012

Academic Editor: Luc Vrancken

Copyright © 2012 Akram Mohammadpouri and S. M. B. Kashani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

By using the operator 𝐿 𝑟 , 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.