An excess sphere theorem
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 26 (1993) no. 2, pp. 175-188.
@article{ASENS_1993_4_26_2_175_0,
     author = {Petersen, Peter and Zhu, Shun-Hui},
     title = {An excess sphere theorem},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {175--188},
     publisher = {Elsevier},
     volume = {Ser. 4, 26},
     number = {2},
     year = {1993},
     doi = {10.24033/asens.1670},
     mrnumber = {1209707},
     zbl = {0771.53024},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.1670/}
}
TY  - JOUR
AU  - Petersen, Peter
AU  - Zhu, Shun-Hui
TI  - An excess sphere theorem
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1993
DA  - 1993///
SP  - 175
EP  - 188
VL  - Ser. 4, 26
IS  - 2
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.24033/asens.1670/
UR  - https://www.ams.org/mathscinet-getitem?mr=1209707
UR  - https://zbmath.org/?q=an%3A0771.53024
UR  - https://doi.org/10.24033/asens.1670
DO  - 10.24033/asens.1670
LA  - en
ID  - ASENS_1993_4_26_2_175_0
ER  - 
%0 Journal Article
%A Petersen, Peter
%A Zhu, Shun-Hui
%T An excess sphere theorem
%J Annales scientifiques de l'École Normale Supérieure
%D 1993
%P 175-188
%V Ser. 4, 26
%N 2
%I Elsevier
%U https://doi.org/10.24033/asens.1670
%R 10.24033/asens.1670
%G en
%F ASENS_1993_4_26_2_175_0
Petersen, Peter; Zhu, Shun-Hui. An excess sphere theorem. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 26 (1993) no. 2, pp. 175-188. doi : 10.24033/asens.1670. http://www.numdam.org/articles/10.24033/asens.1670/

[A1] M. Anderson, Metrics of Positive Ricci Curvature with Large Diameter (Manu. Math., Vol. 68, 1990, pp. 405-415). | MR | Zbl

[A2] M. Anderson, Short Geodesics and Gravitational Instantons (J. Diff. Geom., Vol. 31, 1990, pp. 265-275). | MR | Zbl

[B] A. Besse, Manifolds all of whose Geodesics are Closed, Springer Verlag, Berlin, Heidelberg, New York, 1978. | MR | Zbl

[Be] G. Bessa, Differentiable Sphere Theorem for Ricci Curvature, preprint.

[BK] P. Buser and H. Karcher, Gromov's Almost Flat Manifolds (Asterisque, Vol. 81, 1981, pp. 1-148). | MR | Zbl

[BT] Y. Burago and V. Toponogov, On the Three Dimensional Riemannian Spaces with Bounded Curvature (Matematicheskie Zametki, Vol. 13, 1973, pp. 881-887). | Zbl

[C] S. Cheng, Eigenvalue Comparison Theorems and its Geometric Applications (Math. Z., Vol. 143, 1975, pp. 289-297). | MR | Zbl

[Ce] J. Cerf, Sur les difféomorphismes de la sphère de dimension trois (Lecture Notes in Math. 53, Springer Verlag, Berlin, Heidelberg, New York, 1975). | MR | Zbl

[CG] J. Cheeger and M. Gromov, Collapsing Riemannian Manifolds while Keeping their Curvature Bounded (J. Diff. Geom., Vol. 23, 1986, 309-346). | MR | Zbl

[F] K. Fukaya, A Boundary of the Set of the Riemannian Manifolds with Bounded Curvature and Diameter (J. Diff. Geom., Vol. 28, 1988, pp. 1-21). | MR | Zbl

[Fr] M. Freedman, The Topology of Four Dimensional Manifolds (J. Diff. Geom., Vol. 17, 1982, pp. 457-454). | MR | Zbl

[FY1] K. Fukaya and T. Yamaguchi, Almost Nonpositively Curved Manifolds, preprint.

[FY2] K. Fukaya and T. Yamaguchi, The Fundamental Groups of Almost Nonnegatively Curved Manifolds, preprint.

[GS] R. Greene and K. Shiohama, Convex Functions on Complete Noncompact Manifolds : Differentiable Structures (Ann. Sci. Ec. Norm. Sup., Vol. 14, 1981, pp. 357-367). | Numdam | MR | Zbl

[GK] K. Grove and H. Karcher, How to Conjugate C1-Close Group Actions (Math. Z., Vol. 132, 1973, pp. 11-20). | MR | Zbl

[GP1] K. Grove and P. Petersen, A Pinching Theorem for Homotopy Spheres (Jour. AMS, Vol. 3, 1990, pp. 671-677). | MR | Zbl

[GP2] K. Grove and P. Petersen, Manifolds Near the Boundary of Existence (J. Diff. Geom., Vol. 33, 1991, pp. 379-394). | MR | Zbl

[GrS] K. Grove and K. Shiohama, A Generalized Sphere Theorem (Ann. of Math., Vol. 106, 1977, pp. 201-211). | MR | Zbl

[Ha] R. Hamilton, Three Manifolds with Positive Ricci Curvature (J. Diff. Geom., Vol. 17, 1982, pp. 255-306). | MR | Zbl

[He] J. Hempel, 3-Manifolds (Ann. of Math. Studies, Vol. 86, Princeton Univ. Press, 1976). | MR | Zbl

[KM] M. Kervaire and J. Milnor, Groups of Homotopy Spheres (Ann. of Math., Vol. 77, 1963, pp. 504-537). | MR | Zbl

[M] S. Myers, Riemannian Manifolds with Positive Mean Curvature (Duke Math. J., Vol. 8, 1941, pp. 401-404). | JFM | MR | Zbl

[Mu] J. Munkres, Differentiable Isotopies on the 2-Sphere, (Notices AMS, Vol. 5, 1958, p. 582).

[O1] Y. Otsu, On Manifolds of Small Excess, preprint.

[O2] Y. Otsu, On Manifolds of Positive Ricci Curvature and Large Diameter (Math. Z., Vol. 206, 1991, pp. 255-264). | MR | Zbl

[P] P. Petersen, V, Small Excess and Ricci Curvature, to appear in (J. Geom. Analysis). | Zbl

[PSZ] P. Petersen, Z. Shen and S. Zhu, Manifolds with Small Excess and Bounded Curvature, preprint.

[S] Z. Shen, On Riemannian Manifolds with ε-Maximal Diameter and Bounded Curvature, preprint.

[Sm] S. Smale, Generalized Poincaré Conjecture in Dimensions Greater than Four (Ann. of Math., Vol. 74, 1961, pp. 391-406). | MR | Zbl

[W] J.-Y. Wu, Convergence of Riemannian 3-Manifolds Under Ricci Curvature Bounds, preprint.

[Y] T. Yamaguchi, Collapsing and Pinching Under Lower Curvature Bound (Annals of Math., Vol. 133, 1991, pp. 317-357). | MR | Zbl

Cited by Sources: