ISSN:
1572-9060
Keywords:
Mean exit time
;
Kähler manifold
;
geodesic ball
;
Ricci curvature
;
mean curvature
;
antiholomorphic Ricci curvature
;
complex projective space
;
53C55
;
53C21
;
53C20
;
53C22
;
58C40
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00128339
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