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Comparing the relative volume with a revolution manifold as a model

Authors:	Ana Lluch Vicente Miquel

Institution:	(1) Departament de Matematiques i Informatica, Universitat Jaume I, Campus Penyete Roja, 12071 Castellón, Spain;(2) Departmento de Geometria y Topologia, Universidad de Valencia, C/Dr. Moliner 50, 46100 Burjasot (Valencia), Spain

Abstract:	Given a pair (P, M), whereM is ann-dimensional connected compact Riemannian manifold andP is a connected compact hypersurface ofM, the relative 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 pair, with some bounds on the Ricci curvature ofM and the mean curvature ofP, with respect to that of a model pair $\left( {\mathcal{P},\mathcal{M}} \right)$ where ℳ is a revolution manifold and $\mathcal{P}$ a “parallel” of ℳ. Work partially supported by a DGICYT Grant No. PB91-0324.

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