Lower curvature bounds, Toponogov's theorem, and bounded topology

Uwe Abresch

Annales scientifiques de l'École Normale Supérieure (1985)

  • Volume: 18, Issue: 4, page 651-670
  • ISSN: 0012-9593

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Abresch, Uwe. "Lower curvature bounds, Toponogov's theorem, and bounded topology." Annales scientifiques de l'École Normale Supérieure 18.4 (1985): 651-670. <http://eudml.org/doc/82168>.

@article{Abresch1985,
author = {Abresch, Uwe},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Betti numbers; asymptotically non-negatively curved manifolds; triangle comparison theorem; number of ends},
language = {eng},
number = {4},
pages = {651-670},
publisher = {Elsevier},
title = {Lower curvature bounds, Toponogov's theorem, and bounded topology},
url = {http://eudml.org/doc/82168},
volume = {18},
year = {1985},
}

TY - JOUR
AU - Abresch, Uwe
TI - Lower curvature bounds, Toponogov's theorem, and bounded topology
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1985
PB - Elsevier
VL - 18
IS - 4
SP - 651
EP - 670
LA - eng
KW - Betti numbers; asymptotically non-negatively curved manifolds; triangle comparison theorem; number of ends
UR - http://eudml.org/doc/82168
ER -

References

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  1. [1] L. AHLFORS et L. SARIO, Riemann Surfaces (Princeton Uni. Press, N.J., 1960). Zbl0196.33801MR114911
  2. [2] R. BISHOP et R. CRITTENDEN, Geometry of Manifolds (Academic Press, N. Y., 1964). Zbl0132.16003MR169148
  3. [3] P. BERARD et S. GALLOT, Inégalités Isopérimétriques pour l'Équation de la Chaleur et Application à l'Estimation de quelques Invariants Géométriques (preprint). Zbl0542.53025MR811658
  4. [4] P. BERARD et D. MEYER, Inégalités Isopérimétriques et Applications (Ann. scient. Ec. Norm. Sup., Vol. 15, 1982, pp. 513-542). Zbl0527.35020MR690651
  5. [5] J. CHEEGER et D. EBIN, Comparison Theorems in Riemannian Geometry (North Holland, N. Y., 1975). Zbl0309.53035MR458335
  6. [6] J. CHEEGER et D. GROMOLL, On the Structure of Complete Manifolds of Non-negative Curvature (Ann. of Math., Vol. 96, 1972, pp. 413-443). Zbl0246.53049MR309010
  7. [7] B. DEKSTER et I. KUPKA, Asymptotics of Curvature in a Space of Positive Curvature (J. Diff. Geo., Vol. 15, 1980, pp. 553-568). Zbl0474.53043MR628344
  8. [8] D. ELERATH, An Improved Toponogov Comparison Theorem for Non-negatively Curved Manifolds (J. Diff. Geo., Vol. 15, 1980, pp. 187-216). Zbl0526.53043MR614366
  9. [9] P. EBERLEIN et B. O'NEILL, Visibility Manifolds, (Pacific J. of Math., Vol. 46, 1972, pp. 45-109). Zbl0264.53026MR336648
  10. [10] M. GROMOV, Curvature, Diameter and Betti Numbers (Comm. Math. Helv., Vol. 56, 1981, pp. 179-195). Zbl0467.53021MR630949
  11. [11] W. KLINGENBERG, Riemannian Geometry (De Gruyter, 1982). Zbl0495.53036MR666697
  12. [12] I. RICHARDS, On the Classification of Non-compact Surfaces (Trans. Am. Math. Soc., Vol. 106, 1963, pp. 259-269). Zbl0156.22203MR143186

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