Nonnegative Ricci curvature, small linear diameter growth and finite generation of fundamental groups

Simple item page
dc.creatorSormani, Christina
dc.date1998-09-23
dc.date.accessioned2026-07-07T05:26:07Z
dc.date.available2026-07-07T05:26:07Z
dc.descriptionIn 1968, Milnor conjectured that a complete noncompact manifold with nonnegative Ricci curvature has a finitely generated fundamental group. The author applies the Excess Theorem of Abresch and Gromoll (1990), to prove two theorems. The first states that if such a manifold has small linear diameter growth then its fundamental group is finitely generated. The second states that if such a manifold has an infinitely generated fundamental group then it has a tangent cone at infinity which is not polar. A corollary of either theorem is the fact that if such a manifold has linear volume growth, then its fundamental group is finitely generated.
dc.description12 pages, figures available from author sormani@math.jhu.edu
dc.identifierhttps://arxiv.org/abs/math/9809133
dc.identifierhttp://arxiv.org/abs/math/9809133
dc.identifierJournal of Differential Geom. 54 (2000), no. 3, 547--559
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77434
dc.subjectDifferential Geometry
dc.subject53C21
dc.titleNonnegative Ricci curvature, small linear diameter growth and finite generation of fundamental groups
dc.typetext

Files

Collections

arXiv