|
Curvature, triameter, and beyond
Author(s):
Karsten
Grove;
Steen
Markvorsen
Journal:
Bull. Amer. Math. Soc.
27
(1992),
261-265.
MSC (1980):
Primary 53C20, 51K10, 53C23
MathSciNet review:
1152160
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- [BGP]
- Y. Burago, M. Gromov, and G. Perelman, Aleksandrov's spaces with curvatures bounded from below {\rm I}, Uspekhi Mat. Nauk. MR
- [CE]
- J. Cheeger and D. G. Ebin, Comparison theorems in Riemannian geometry, North-Holland Math Library, vol.~9, North-Holland, Amsterdam, 1975. MR 458335
- [GG]
- D. Gromoll and K. Grove, A generalization of Berger's rigidity theorem for positively curved manifolds, Ann. Sci. \'Ecole. Norm. Sup. \textbf{20} (1987), 227--239. MR 911756
- [G]
- M. Gromov, Filling Riemannian Manifolds, J. Differential Geom. \textbf{18} (1983), 1--148. MR 697984
- [G1]
- K. Grove, \emph{Metric differential geometry}, Differential Geometry (V. L. Hansen, ed.) vol.~vol. 1263, Springer-Verlag, 1987 pp.~171--227. MR 905882
- [G2]
- K. Grove, \emph{Metric and topological measurements of manifolds}, Springer-Verlag, 1991 pp.~511--519. MR 1159238
- [GM]
- K. Grove and S. Markvorsen, Metric invariants for the Riemannian recognition program via Aleksandrov geometry, preprint. MR
- [GP1]
- K. Grove and P. Petersen V, Homotopy types of positively curved manifolds with large volume, Amer. J. Math. \textbf{110} (1988), 1183--1188. MR 970124
- [GP2]
- K. Grove and P. Petersen V, A pinching theorem for homotopy spheres, J. Amer. Math. Soc. \textbf{3} (1990), 671--677. MR 1049696
- [GP3]
- K. Grove and P. Petersen V, Manifolds near the boundary of existence, J. Differential Geom. \textbf{33} (1991), 379--394. MR 1094462
- [GP4]
- K. Grove and P. Petersen V, Volume comparison \`a la Aleksandrov, Acta. Math. MR
- [GPW]
- K. Grove, P. Petersen, and J.-Y. Wu, Geometric finiteness theorems via controlled topology, Invent. Math. \textbf{99} (1990), 205--213. MR 1029396
- [GS]
- K. Grove and K. Shiohama, A generalized sphere theorem, Ann. of Math. (2) \textbf{106} (1977), 201--211. MR 500705
- [H]
- E. Hille, Remarks on transfinite diameters, J. Analyse Math. \textbf{14} (1965), 209--224. MR 199690
- [K1]
- M. Katz, The filling radius of two-point homogeneous spaces, J. Differential Geom. \textbf{18} (1983), 505--511. MR 723814
- [K2]
- M. Katz, The rational filling radius of complex projective spaces, preprint. MR 1137947
- [K3]
- M. Katz, The first diameters of $3$-manifolds of positive scalar curvature, Proc. Amer. Math. Soc. \textbf{104} (1988), 591--595. MR 962834
- [N]
- F. Nielsen, On the sum of distances between $n$ points on the sphere {\rm (Danish)}, Nordisk Tidskr. Mat. \textbf{13} (1965), 45--50. MR
- [O]
- Y. Otsu, On manifolds of small excess, Amer. J. Math. MR 1254733
- [OSY]
- Y. Otsu, K. Shiohama, and T. Yamaguchi, A new version of differentiable sphere theorem, Invent. Math. \textbf{98} (1989), 219--228. MR 1016261
- [PZ]
- P. Petersen and Zhu, \emph{An excess sphere theorem}. MR
- [R]
- W. Rinow, Die Innere Geometrie der Metrischen R{\"a}ume (1961), Springer-Verlag, 1961. MR 123969
- [SY]
- K. Shiohama and T. Yamaguchi, \emph{Positively curved manifolds with restricted diameters} vol.~8, Academic Press, Boston, MA, 1989 pp.~345--350. MR 1040534
- [T]
- F. Toth, On the sum of distances determined by a pointset, Acta. Math. Acad. Sci. Hungar. \textbf{7} (1957), 397--401. MR 107212
- [U]
- P. Urysohn, Notes suppl\'ementaires, Fund. Math. \textbf{8} (1926), 352--356. MR
- [W]
- F. Wilhelm, On the filling radius of positively curved manifolds, Invent. Math. \textbf{107} (1992), 653--668. MR 1150606
- [Y]
- T. Yamaguchi, Collapsing and pinching under a lower curvature bound, Ann. of Math. (2) \textbf{133} (1991), 317--357. MR 1097241
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1980):
53C20, 51K10, 53C23
Retrieve articles in all Journals with MSC
(1980):
53C20, 51K10, 53C23
Additional Information:
DOI:
10.1090/S0273-0979-1992-00308-7
PII:
S 0273-0979(1992)00308-7
|
