On the fundamental group of open manifolds with nonnegative Ricci curvature (Q1423917)

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)].