Ricci Curvature and Fundamental Group*

Abstract

By refined volume estimates in terms of Ricci curvature, the two results due to J. Milnor (1968) are generalized.

Keywords

Ricci curvature / Fundamental group / Volume growth / 53C20 / 20F34

References

[1] Bishop Notices Amer. Math. Soc., 1963, 10: 364

[2] Greene, R. E. and Wu, H., Function theory on manifold which possess a pole, Lecture Notes in Math., 699, Springer-Verlag, 1979.

[3] Gao Invent. Math., 1986, 85: 637

[4] Lohkamp Ann. Math., 1994, 140: 655

[5] Milnor J. Diff. Geom., 1968, 2: 1

[6] Preissman Comment. Math. Helv., 1942, 15: 175

[7] Xin, Y. L., Geometry of Harmonic Maps, Birkhäuser, 1996.

[8] Yang Bull. Austral. Math., 1996, 54: 483