On the fundamental group of open manifolds with nonnegative Ricci curvature
type: Item
instance of: scholarly article
title: On the fundamental group of open manifolds with nonnegative Ricci curvature
zbMATH Open document ID: 1057.53024
DOI: 10.1142/S0252959903000463
author: Zuoqin Wang
author: Fangyun Yang
author: Senlin Xu
published in: Chinese Annals of Mathematics. Series B
publication date: 2004-03-07T00:00:00Z
review text: A famous conjecture by J. Milnor states that a complete noncompact Riemannian manifold \ \(\left\langle M^{n},g\right\rangle \) with nonnegative Ricci curvature has finite fundamental group. The authors obtain results supporting Milnor's conjecture. The main theorem states that Milnor's conjecture is true if \(M^{n}\) has a small ray density function: \(\lim D\left( r\right) /r<2S_{n},\) where \(S_{n}=\frac{1}{4}\frac{1}{n-1}\left( \frac {n-2}{n}\right) ^{n-1}\). This can be viewed as a generalization of a theorem by \textit{C. Sormani} [J. Differ. Geom. 54, No. 3, 547--559 (2000; Zbl 1035.53045)].
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 2052045
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: Ricci curvature
zbMATH Keywords: fundamental group
reviewed by: Igor G. Nikolaev
MaRDI profile type: Publication
full work available at URL: s0252959903000463
OpenAlex ID: W2396835591
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description: scientific article; zbMATH DE number 2052045