Skip to main content
Log in

On the filling radius of positively curved manifolds

  • Published:
Inventiones mathematicae Aims and scope

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

  • [CE] Cheeger, J., Ebin, D.G.: Comparison Theorems in Riemannian Geometry. (North-Holland Math. Libr., vol. 9) Amsterdam Oxford: North-Holland 1975

    Google Scholar 

  • [GW1] Greene, R.E., Wu, H.: On the subharmonicity and plurisubharmonicity of geodesically convex functions. Indiana Univ. Math. J.22, 641–653 (1973)

    Google Scholar 

  • [GW2] Greene, R.E., Wu, H.: Integrals of subharmonic functions on manifolds of nonnegative curvature. Invent. Math.27, 265–298 (1974)

    Google Scholar 

  • [GW3] Greene, R.E., Wu, H.:C functions and manifolds of positive curvature. Acta Math.137, 209–245 (1976)

    Google Scholar 

  • [G1] Gromov, M.: Groups of polynomial growth and expanding maps. Publ. Math., Inst. Hautes Étud. Sci.53, 53–73 (1981)

    Google Scholar 

  • [G2] Gromov, M.: Filling Riemannian manifolds. J. Differ. Geom.18, 1–147 (1983)

    Google Scholar 

  • [GLP] Gromov, M., Lafontaine, J., Pansu, P.: Structures métriques pour les variétés riemanniennes. Paris: Cedic/Fernand Nathan 1981

    Google Scholar 

  • [GP1] Grove, K., Petersen, P., V.: Manifolds near the boundary of existence. J. Differ. Geom.33, 379–394 (1991)

    Google Scholar 

  • [GP2] Grove, K., Petersen, P., V.: On the excess of metric spaces and manifolds. (Preprint)

  • [GP3] Grove, K., Petersen, P., V: Volume comparison à la Aleksandrov. (Preprint)

  • [GS] Grove, K., Shiohama, K.: A generalized sphere theorem. Ann. Math.106, 201–211 (1977)

    Google Scholar 

  • [K1] Katz, M.: The Filling radius of two-point homogeneous spaces. J. Differ. Geom.18, 505–511 (1983)

    Google Scholar 

  • [K2] Katz, M.: The Rational Filling Radius of Complex Projective Space. Topology Appl. (to appear)

  • [OSY] Otsu, Y., Shiohama, K., Yamaguchi, T.: A new version of differentiable sphere theorem. Invent. Math.98, 219–228 (1989)

    Google Scholar 

  • [R] Rinow, W.: Innere Geometrie der Metrischen Räume. Berlin: Springer 1961

    Google Scholar 

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

    Google Scholar 

  • [W] Wu, H.: Manifolds of Partially Positive Curvature. Indiana Univ. Math. J.36 (no. 3), 525–548 (1987)

    Google Scholar 

  • [Y] Yamaguchi, T.: Collapsing and pinching under a lower curvature bound. Ann. Math.133, 317–357 (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Oblatum 19-III-1991 & 19-VIII-1991

The author is an Alfred P. Sloan Doctoral Dissertation Fellow. This work is part of a Ph.D. thesis directed by Karsten Grove.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wilhelm, F.H. On the filling radius of positively curved manifolds. Invent Math 107, 653–668 (1992). https://doi.org/10.1007/BF01231906

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01231906

Keywords

Navigation