Bounded harmonic functions and positive Ricci curvature
type: Item
instance of: scholarly article
title: Bounded harmonic functions and positive Ricci curvature
zbMATH Open document ID: 0604.30051
DOI: 10.1007/BF01162345
author: Harold Donnelly
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173699
review text: Let M be a complete Riemannian manifold. It is known that if M has non- negative Ricci curvature then every bounded harmonic function is constant. This result is extended to the case of a non-negative curvature outside of a compact subset of M and it is then proved that the space of bounded harmonic functions is finite dimensional. Actually it is proved that the map \(f\to df\) from the space of bounded harmonic functions on the space of harmonic one forms has its range in a finite dimensional space and the result follows from the fact that the kernel of this map is one dimensional.
Mathematics Subject Classification ID: 30F15
Mathematics Subject Classification ID: 31A05
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 3975336
zbMATH Keywords: Ricci curvature
reviewed by: Jean Lacroix
MaRDI profile type: Publication
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OpenAlex ID: W2087197205
description: scientific article; zbMATH DE number 3975336