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RESEARCH PRODUCT

A comparison theorem for the mean exit time from a domain in a K�hler manifold

Vicente MiquelVicente Palmer

subject

Comparison theoremRiemann curvature tensorGeodesicComplex projective spaceMathematical analysisKähler manifoldCurvaturesymbols.namesakesymbolsMathematics::Differential GeometryGeometry and TopologyAnalysisRicci curvatureMathematicsScalar curvature

description

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.

https://doi.org/10.1007/bf00128339