Liouville-type theorem for the drifting Laplacian operator
type: Item
instance of: scholarly article
title: Liouville-type theorem for the drifting Laplacian operator
zbMATH Open document ID: 1217.58012
author: Guangyue Huang
author: Congcong Zhang
author: Jing Zhang
published in: Archiv der Mathematik
publication date: 2011-06-01T00:00:00Z
review text: Consider a manifold \((M, g, e ^{-f} dV)\) with a smooth measure. The authors obtain gradient estimates for positive harmonic functions of the drifting Laplacian. If the \(\infty\)-Bakry-Emery Ricci tensor is bounded from below and \(|\nabla f|\) is bounded, they obtain a Liouville-type theorem, extending in this way the classical result by \textit{S. Y. Cheng} and \textit{S.-T. Yau} [Commun. Pure Appl. Math. 28, 333--354 (1975; Zbl 0312.53031)].
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 58J35
zbMATH DE Number: 5902955
zbMATH Keywords: gradient estimate
zbMATH Keywords: positive solution
zbMATH Keywords: Bakry-Emery Ricci tensor
MaRDI profile type: Publication
full work available at URL: s00013-011-0242-5
OpenAlex ID: W2147305125
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DOI: 10.1007/S00013-011-0242-5
description: scientific article; zbMATH DE number 5902955