Infinity behavior of bounded subharmonic functions on Ricci non-negative manifolds
type: Item
instance of: scholarly article
title: Infinity behavior of bounded subharmonic functions on Ricci non-negative manifolds
zbMATH Open document ID: 1073.53048
publication date: 2004-11-26T00:00:00Z
review text: The author studies bounded subharmonic functions on complete Riemannian manifolds of non-negative Ricci curvature. He derives the formula \(\lim_{r\to\infty}\int_{B_x(r)} \Delta h\,dv=0\) for such functions. Further, a result by \textit{P.~Li} [Ann.\ Math.\ 124, 1--21 (1986; Zbl 0613.58032)] says that, intuitively speaking, such a function approaches its supremum at infinity when taking its average over geodesic balls. Here, the author investigates whether a pointwise limit at infinity exists. The answer is negative in general, but positive under some additional conditions on the function and the volume growth of the manifold.
reviewed by: Eric Boeckx
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 58J37
zbMATH DE Number: 2119272
zbMATH Keywords: subharmonic functions
zbMATH Keywords: non-negative Ricci curvature
zbMATH Keywords: volume growth
author: Baoqiang Wu
MaRDI profile type: Publication
full work available at URL: s10114-003-0242-x
OpenAlex ID: W2313274852
cites work: Large time behavior of the heat equation on complete manifolds with non- negative Ricci curvature
cites work: Linear growth harmonic functions on complete manifolds with nonnegative Ricci curvature
cites work: Harmonic functions of linear growth on Kähler manifolds with nonnegative Ricci curvature
cites work: Linear growth harmonic functions on a complete manifold
cites work: On the parabolic kernel of the Schrödinger operator
cites work: Differential equations on riemannian manifolds and their geometric applications
DOI: 10.1007/S10114-003-0242-X
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 2119272