Abstract
In this note, we show that if M n is a nonnegatively Bakry–Émery-Ricci curved manifold with bounded potential function, any finitely generated subgroup of the fundamental group of M has polynomial growth of degree less than or equal to n.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Bakry and M. Émery, Diffusion hypercontractivitives, in Séminaire de Probabilités XIX 177-206, 1983/84, Lect. Notes in Math. 1123, Springer, Berlin, 1985.
B. Chow, P. Lu, and L. Ni, Hamilton’s Ricci flow, Graduate Studies in Mathematics 77, American Mathematical Society, Provindence, RI, 2006
Fernández-López M., García-Río E.: A remark on compact Ricci solitons. Math. Ann. 340, 893–896 (2008)
Ho P.T.: A remark on complete non-expanding Ricci solitons. Arch. Math. 91, 284–288 (2008)
Li X.-M.: On extensions of Myers’ theorem. Bull. London Math. Soc. (4) 27, 392–396 (1995)
Lott J.: Some geometric properties of the Bakry–Émery Ricci tensor. Comment. Math. Helv. 78, 865–883 (2003)
Milnor J.: A note on curvature and fundamental group. J. Diff. Geom. 2, 1–7 (1968)
Qian Z.: Estimates for weighted volumes and applications. Quart. J. Math. Oxford Ser. (2) 48, 235–242 (1997)
G. F. Wei and W. Wylie, Comparison geometry for the Bakry–Émery Ricci tensor, arXiv:math.DG/0706.1120v1.
Wylie W.: Complete shrinking Ricci solitons have finite fundamental group. Proc. Amer. Math. Soc. 136, 1803–1806 (2008)
Zhang Z.L.: On the Finiteness of the fundamental group of a compact shrinking Ricci soliton. Colloq. Math. 107, 297–299 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yang, N. A note on nonnegative Bakry–Émery Ricci curvature. Arch. Math. 93, 491–496 (2009). https://doi.org/10.1007/s00013-009-0062-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-009-0062-z