A comparison theorem for the mean exit time from a domain in a Kähler manifold
type: Item
instance of: scholarly article
title: A comparison theorem for the mean exit time from a domain in a Kähler manifold
zbMATH Open document ID: 0773.53027
DOI: 10.1007/BF00128339
author: Vicente Miquel
author: Vicente Palmer
published in: Annals of Global Analysis and Geometry
publication date: 1993-04-01T00:00:00Z
review text: The main purpose of this paper is to study a domain \(\Omega\) of a Kähler manifold with Ricci and antiholomorphic Ricci curvature bounded from below. The authors consider bounds on the mean and \(JN\)-mean curvature of its boundary. They prove a comparison theorem between the mean exit time function \(E(x)\) defined on \(\Omega\) with the mean exit time \(E^ \lambda_ R(\underline x)\) from the geodesic ball of radius \(R\) of the complex projective space \(CP^ n(\lambda)\). The equality \(E(x)=E^ \lambda_ R(\underline x)\) gives a characterization of the geodesic ball among the domains \(\Omega\). It is proved also a comparison theorem for the mean curvature of hypersurfaces parallel to the boundary of \(\Omega\) using the Index Lemma for submanifolds.
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 147451
zbMATH Keywords: antiholomorphic Ricci curvature
zbMATH Keywords: mean exit time function
zbMATH Keywords: geodesic ball
zbMATH Keywords: mean curvature
reviewed by: Neda Bokan
MaRDI profile type: Publication
cites work: Q5341449
cites work: Q3344779
cites work: Eigenvalue comparison theorems and its geometric applications
cites work: Q5182804
cites work: Q5342182
cites work: Volume estimates for real hypersurfaces of a Kaehler manifold with strictly positive holomorphic sectional and antiholomorphic Ricci curvatures
cites work: Bounds for the first Dirichlet eigenvalue of domains in Kaehler manifolds
cites work: $C^\infty$ approximations of convex, subharmonic, and plurisubharmonic functions
cites work: Comparison theorems for the volumes of tubes as generalizations of the Weyl tube formula
cites work: A general comparison theorem with applications to volume estimates for submanifolds
cites work: Q3700423
cites work: On a lower bound for the first eigenvalue of the Laplace operator on a riemannian manifold
cites work: On the mean exit time from a minimal submanifold
cites work: On the volume of positively curved Kähler manifolds
full work available at URL: https://doi.org/10.1007/bf00128339
OpenAlex ID: W1991434977
description: scientific article; zbMATH DE number 147451