Generalized Liouville properties of manifolds
type: Item
instance of: scholarly article
title: Generalized Liouville properties of manifolds
zbMATH Open document ID: 0884.58032
published in: Mathematical Research Letters
publication date: 1998-03-19T00:00:00Z
review text: The authors announce several results published elsewhere on generalized Liouville theorems on manifolds. The main result is the following theorem proved in [\textit{T. H. Colding} and \textit{W. P. Minicozzi}, Ann. Math., II. Ser. 146, No. 3, 725-747 (1997)] which was conjectured by \textit{S. T. Yau} [Proc. Symp. Pure Math. 54, Part 1, 1-28 (1993; Zbl 0801.53001)]: For an open manifold with nonnegative Ricci curvature the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional. This theorem is a consequence of a much more general result which is also presented in the paper.
reviewed by: Witold Mozgawa
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 991909
zbMATH Keywords: harmonic function
zbMATH Keywords: polynomial growth
zbMATH Keywords: Liouville theorem
zbMATH Keywords: Neumann Poincaré inequality
author: Tobias Holck Colding
author: William P. II Minicozzi
MaRDI profile type: Publication
full work available at URL: mrl.1996.v3.n6.a1
OpenAlex ID: W2062660121
DOI: 10.4310/MRL.1996.V3.N6.A1
description: scientific article; zbMATH DE number 991909