Abstract
Let M be a Kähler 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.
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Work partially supported by a DGICYT Grant No. PS87-0115-C03-01.
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Miquel, V., Palmer, V. A comparison theorem for the mean exit time from a domain in a Kähler manifold. Ann Glob Anal Geom 10, 73–80 (1992). https://doi.org/10.1007/BF00128339
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DOI: https://doi.org/10.1007/BF00128339
Key words
- Mean exit time
- Kähler manifold
- geodesic ball
- Ricci curvature
- mean curvature
- antiholomorphic Ricci curvature
- complex projective space