Skip to main content
Log in

A comparison-estimate of Toponogov type for Ricci curvature

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • [A-G] Abresch, U., Gromoll, D.: On complete manifolds with nonnegative Ricci curvature. Journal of A.M.S.3, 355–374 (1990)

    Google Scholar 

  • [A-C] Anderson, M., Cheeger, J.:C α-compactness for manifolds with Ricci curvature and injectivity radius bounded below. J. Diff. Geom.35, 265–281 (1992)

    Google Scholar 

  • [B1] Brocks, R.: Abstandsfunktion, Riccikrümmung und injektivitätsradius. Diplomarbeit, University of Münster, 1993

  • [B2] Brocks, R.: Convexity and Ricci curvature. C.R.A.S., tome 319 Serie 1, 73–75 (1994)

    Google Scholar 

  • [C-E] Cheeger, J., Ebin, D.: Comparison theorems in Riemannian geometry. North-Holland, Amsterdam, 1975

    Google Scholar 

  • [C-G] Cheeger, J., Gromoll, D.: The splitting theorem for manifolds of nonnegative Ricci curvature. J. Differential Geom.6, 119–129 (1971)

    Google Scholar 

  • [D-S-W] Dai, X., Shen, Z., Wei, G.: Negative Ricci curvature and isometry group. to appear in Duke Math J. (1994)

  • [S-Y] Sha, J.P., Yang, D.Y.: Examples of metrics of positive Ricci curvature. J. Differential Geom.29, 95–103 (1989)

    Google Scholar 

  • [S] Shen, Z.: Finiteness and vanishing theorems for complete open riemannian manifolds. Bull. Amer. Math. Soci.21, 241–244 (1989)

    Google Scholar 

  • [S-W] Shen, Z., Wei, G.: Volume growth and finite topological type. Proc. Symposia in Pure Math.54, 539–549 (1993)

    Google Scholar 

  • [W] Wei, G.: Ricci curvature and betti numbers, to appear J. Geom. Analysis

Download references

Author information

Authors and Affiliations

Authors

Additional information

Partially supported by NSF Grant # DMS9204267 and Alfred P. Sloan Fellowship

Partially supported by NSF Grant # DMS9409166. Both authors would like to thank MSRI for additional support and hospitality during the fall of 1993

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dai, X., Wei, G. A comparison-estimate of Toponogov type for Ricci curvature. Math. Ann. 303, 297–306 (1995). https://doi.org/10.1007/BF01460991

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01460991

Mathematics Subject Classification (1991)

Navigation