In 1968, Milnor conjectured that a complete noncompact manifold, M", with nonnegative
Ricci curvature has a finitely generated fundamental group [11]. This was proven for a …

In this paper we consider nonnegatively curved finite dimensional Alexandrov spaces such
that unit balls have volumes uniformly bounded from below away from zero. We study the …

arXiv:math/0612107v1 [math.DG] 4 Dec 2006 Page 1 arXiv:math/0612107v1 [math.DG] 4 Dec
2006 Manifolds with A Lower Ricci Curvature Bound Guofang Wei ∗ Abstract This paper is a …

We prove that an open noncollapsed manifold with nonnegative Ricci curvature and linear
volume growth always splits off a line at infinity. This completes the final step to prove the …

We give a definition of convergence of differential of Lipschitz functions with respect to
measured Gromov-Hausdorff topology. As their applications, we give a characterization of …

Harmonic functions on manifolds with nonnegative Ricci curvature and linear volume growth
Page 1 Pacific Journal of Mathematics HARMONIC FUNCTIONS ON MANIFOLDS WITH …

In this paper we prove that a complete noncompact manifold with nonnegative Ricci
curvature has a trivial codimension one homology unless it is a flat normal bundle over a …

A Ricci curvature bound is weaker than a sectional curvature bound but stronger than a
scalar curvature bound. Ricci curvature is also special that it occurs in the Einstein equation …

Understanding the relationships between geometry and topology is a central theme in
Riemannian geometry. We establish two results on the fundamental groups of open …

We survey all results concerning the topology of complete noncompact Riemannian
manifolds with nonnegative Ricci curvature that have no additional conditions other than …