Skip to main content
SpringerLink
Log in

Mainfolds with small excess and bounded curvature

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  • [B] Besse, A.: Manifolds all of whose geodesics are closed, Berlin Heidelberg New York: Springer 1978

    MATH  Google Scholar 

  • [F] Fukaya, K.: A boundary of the set of the Riemannian manifolds with bounded curvature and diameter, J. Differ. Geom.28, 1–21 (1988)

    MATH  MathSciNet  Google Scholar 

  • [G] Gromov, M.: Groups of polynomial growth. Publ. Math., Inst. Hantes Étud. Sci.53, 53–73 (1981)

    MATH  MathSciNet  Google Scholar 

  • [GP1] Grove, K., Petersen, P., V.: On the excess of metric spaces and manifolds (Preprint)

  • [GP2] Grove, K., Petersen, P. V.: A pinching theorem for homotopy spheres. J. Am. Math. Soc.3, 671–677 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  • [GP3] Grove, K., Petersen, P. V.: Manifolds near the boundary of existence J. Differ. Geom.33, 379–394 (1991)

    MATH  MathSciNet  Google Scholar 

  • [H] Hempel, J.: 3-manifolds. (Ann. Math. Stud. vol. 86) Princeton: Princeton University Press 1976

    MATH  Google Scholar 

  • [O] Otsu, Y: On manifolds of small excess. (Preprint)

  • [P] Petersen, P.: Small excess and Ricci curvature. J. Geom. Anal. (to appear)

  • [PZ] Petersen, P., Zhu, S.: An excess sphere theorem. Ann. Sci. Ec. Norm. Super. (to appear)

  • [S] Shen, Z.: On Riemannian manifolds with ε-maximal diameter and bounded curvature. (Preprint)

  • [SY] Shiohama, S., Yamaguchi, T.: Positively curved manifolds with restricted diameter. In: Shiohama, K. (ed.) Geometry of Manifolds (Perspect. Math. vol. 8, pp. 345–350) Boston, MA: Academic Press 1989

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles, 90024, Los Angeles, CA, USA

    Peter Petersen V & Shunhui Zhu

  2. Department of Mathematics, The University of Michigan, 48109, Ann Arbor, MI, USA

    Zhongmin Shen

Authors
  1. Peter Petersen V
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhongmin Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shunhui Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Partially supported by NSF and A.P. Sloan foundation

Partially supported by NSF

Rights and permissions

Reprints and permissions

About this article

Cite this article

Petersen V, P., Shen, Z. & Zhu, S. Mainfolds with small excess and bounded curvature. Math Z 212, 581–585 (1993). https://doi.org/10.1007/BF02571677

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02571677

Keywords

Search

Navigation