COMPARING THE RELATIVE VOLUME WITH A REVOLUTION MANIFOLD AS A MODEL

Given a pair (P, M), where M is an n-dimensional connected compact Rie mannian manifold and P is a connected compact hypersurface of M, the r elative volume of (P, M) is the quotient volume(P)/volume(M). In this paper we give a comparison theorem for the relative volume of such a p air, with some bounds on the Ricci curvature of M and the mean curvatu re of P, with respect to that of a model pair (P,M) where M is a revol ution manifold and P a ''parallel'' of M.