6533b828fe1ef96bd1288238

RESEARCH PRODUCT

Volume estimate for a cone with a submanifold as vertex

Fernando GiménezFernando Giménez

subject

Mean curvature flowPure mathematicsMean curvatureMathematics::Complex VariablesMathematical analysisSubmanifoldHypersurfaceVertex (curve)Mathematics::Differential GeometryGeometry and TopologySectional curvatureMathematics::Symplectic GeometryRicci curvatureMathematicsScalar curvature

description

We give some estimates for the volume of a cone with vertex a submanifold P of a Riemannian or Kaehler manifold M. The estimates are functions of bounds of the mean curvature of P and the sectional curvature of M. They are sharp on cones having a basis which is contained in a tubular hypersurface about P in a space form or in a complex space form.

yearjournalcountryeditionlanguage
1992-11-01Journal of Geometry
https://doi.org/10.1007/bf01225767