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Finiteness of fundamental groups for manifolds with sign-changing Ricci curvature
Abstract
Let M be a complete open κ noncollapsed Riemannian manifold and have Ricci curvature bounded from below. If the negative part of its Ricci curvature goes to zero sufficiently rapidly at infinity in terms of the volume noncollapse constant and dimension n, then the fundamental group of M is finite. When the Ricci curvature is nonnegative, the result agrees with the classical conclusion of [Peter Li, 1986].
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BibTeX
@misc{qin2026finiteness,
title = {{Finiteness of fundamental groups for manifolds with sign-changing Ricci curvature}},
author = {Lang Qin},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.12700},
eprint = {2611.12700},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.12700},
}
RIS
TY - UNPB
TI - Finiteness of fundamental groups for manifolds with sign-changing Ricci curvature
AU - Lang Qin
PY - 2026
DA - 2026/11/09
PB - arXiv
DO - 10.48550/arxiv.2611.12700
UR - https://arxiv.org/abs/2611.12700
AB - Let M be a complete open κ noncollapsed Riemannian manifold and have Ricci curvature bounded from below. If the negative part of its Ricci curvature goes to zero sufficiently rapidly at infinity in terms of the volume noncollapse constant and dimension n, then the fundamental group of M is finite. When the Ricci curvature is nonnegative, the result agrees with the classical conclusion of [Peter Li, 1986].
ER -