Nonnegative Ricci curvature and escape rate gap

2020/09/01 by Jiayin Pan, Pan, Jiayin · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2009.00226

openalex publication_date 2020/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be an open n-manifold of nonnegative Ricci curvature and let p∈ M. We show that if (M,p) has escape rate less than some positive constant ε(n), that is, minimal representing geodesic loops of π₁(M,p) escape from any bounded balls at a small linear rate with respect to their lengths, then π₁(M,p) is virtually abelian. This generalizes the author's previous work, where the zero escape rate is considered.

Citations

• Lower Bounds on Ricci Curvature and the Almost Rigidity of Warped Products
• Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications
• Nonnegative Ricci curvature, almost stability at infinity, and structure of fundamental groups

Cited by

• Fundamental groups of open manifolds with nonnegative Ricci curvature and universal cover Euclidean volume growth

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