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A comparison theorem for the mean exit time from a domain in a K�hler manifold
Vicente MiquelVicente Palmersubject
Comparison theoremRiemann curvature tensorGeodesicComplex projective spaceMathematical analysisKähler manifoldCurvaturesymbols.namesakesymbolsMathematics::Differential GeometryGeometry and TopologyAnalysisRicci curvatureMathematicsScalar curvaturedescription
Let M be a Kahler manifold with Ricci and antiholomorphic Ricci curvature bounded from below. Let ω be a domain in M with some bounds on the mean and JN-mean curvatures of its boundary ∂ω. The main result of this paper is a comparison theorem between the Mean Exit Time function defined on ω and the Mean Exit Time from a geodesic ball of the complex projective space ℂℙ n (λ) which involves a characterization of the geodesic balls among the domain ω. In order to achieve this, we prove a comparison theorem for the mean curvatures of hypersurfaces parallel to the boundary of ω, using the Index Lemma for Submanifolds.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1992-01-01 | Annals of Global Analysis and Geometry |