References
[CE] Cheeger, J., Ebin, D.G.: Comparison Theorems in Riemannian Geometry. (North-Holland Math. Libr., vol. 9) Amsterdam Oxford: North-Holland 1975
[GW1] Greene, R.E., Wu, H.: On the subharmonicity and plurisubharmonicity of geodesically convex functions. Indiana Univ. Math. J.22, 641–653 (1973)
[GW2] Greene, R.E., Wu, H.: Integrals of subharmonic functions on manifolds of nonnegative curvature. Invent. Math.27, 265–298 (1974)
[GW3] Greene, R.E., Wu, H.:C ∞ functions and manifolds of positive curvature. Acta Math.137, 209–245 (1976)
[G1] Gromov, M.: Groups of polynomial growth and expanding maps. Publ. Math., Inst. Hautes Étud. Sci.53, 53–73 (1981)
[G2] Gromov, M.: Filling Riemannian manifolds. J. Differ. Geom.18, 1–147 (1983)
[GLP] Gromov, M., Lafontaine, J., Pansu, P.: Structures métriques pour les variétés riemanniennes. Paris: Cedic/Fernand Nathan 1981
[GP1] Grove, K., Petersen, P., V.: Manifolds near the boundary of existence. J. Differ. Geom.33, 379–394 (1991)
[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)
[K1] Katz, M.: The Filling radius of two-point homogeneous spaces. J. Differ. Geom.18, 505–511 (1983)
[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)
[R] Rinow, W.: Innere Geometrie der Metrischen Räume. Berlin: Springer 1961
[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
[W] Wu, H.: Manifolds of Partially Positive Curvature. Indiana Univ. Math. J.36 (no. 3), 525–548 (1987)
[Y] Yamaguchi, T.: Collapsing and pinching under a lower curvature bound. Ann. Math.133, 317–357 (1991)
Author information
Authors and Affiliations
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
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
Issue Date:
DOI: https://doi.org/10.1007/BF01231906