On some Liouville theorems on noncompact Riemannian manifolds
type: Item
instance of: scholarly article
title: On some Liouville theorems on noncompact Riemannian manifolds
zbMATH Open document ID: 0946.58015
DOI: 10.1007/BF02732362
author: Yanyan Li
published in: Siberian Mathematical Journal
publication date: 2000-04-13T00:00:00Z
review text: The author considers the problem of existence of bounded harmonic functions, i.e., solutions to the equation \(\Delta u =0\) on noncompact manifolds where \(\Delta\) is the Laplace-Beltrami operator. For manifolds which look at infinity like a product of Riemannian manifolds and a line, a criterion for the existence of such functions is given. This criterion is also generalized for the existence of bounded solutions to the equation \(\Delta u = c u\) on the same manifolds.
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 58J60
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 1431738
zbMATH Keywords: harmonic function
zbMATH Keywords: Liouville theorem
Wikidata QID: Q115391837
reviewed by: I. A. Taimanov
MaRDI profile type: Publication
cites work: Q3780159
cites work: Q4029891
cites work: On Nonexistence of any λ0-invariand positive harmonic function, a counter example to stroock' conjecture
description: scientific article; zbMATH DE number 1431738