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Comparing the relative volume with a revolution manifold as a model
Vicente MiquelAna Lluchsubject
CombinatoricsComparison theoremMean curvatureHypersurfaceGeneral MathematicsMathematical analysisMathematics::Differential GeometryRiemannian manifoldRicci curvatureQuotientManifoldMathematicsScalar curvaturedescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1993-10-01 | Israel Journal of Mathematics |