Manifolds with quadratic curvature decay and slow volume growth

John Lott; Zhongmin Shen

Annales scientifiques de l'École Normale Supérieure (2000)

  • Volume: 33, Issue: 2, page 275-290
  • ISSN: 0012-9593

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Lott, John, and Shen, Zhongmin. "Manifolds with quadratic curvature decay and slow volume growth." Annales scientifiques de l'École Normale Supérieure 33.2 (2000): 275-290. <http://eudml.org/doc/82515>.

@article{Lott2000,
author = {Lott, John, Shen, Zhongmin},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {topological obstructions; volume growth; quadratic curvature decay; topological finiteness},
language = {eng},
number = {2},
pages = {275-290},
publisher = {Elsevier},
title = {Manifolds with quadratic curvature decay and slow volume growth},
url = {http://eudml.org/doc/82515},
volume = {33},
year = {2000},
}

TY - JOUR
AU - Lott, John
AU - Shen, Zhongmin
TI - Manifolds with quadratic curvature decay and slow volume growth
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2000
PB - Elsevier
VL - 33
IS - 2
SP - 275
EP - 290
LA - eng
KW - topological obstructions; volume growth; quadratic curvature decay; topological finiteness
UR - http://eudml.org/doc/82515
ER -

References

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  2. [2] Bonahon F., Bouts des variétés hyperboliques de dimension 3, Ann. of Math. 124 (1986) 71-158. Zbl0671.57008MR88c:57013
  3. [3] Cheeger J., Critical points of distance functions and applications to geometry, in : Geometric Topology : Recent Developments, Lecture Notes in Math., Vol. 1504, Springer, New York, 1991, pp. 1-38. Zbl0771.53015MR94a:53075
  4. [4] Cheeger J., Gromov M., On the characteristic numbers of complete manifolds of bounded curvature and finite volume, in : Differential Geometry and Complex Analysis, Springer, Berlin, 1985, pp. 115-154. Zbl0592.53036MR86h:58131
  5. [5] Cheeger J., Gromov M., Collapsing Riemannian manifolds while keeping their curvature bounded I, J. Differential Geom. 23 (1986) 309-346. Zbl0606.53028MR87k:53087
  6. [6] Cheeger J., Gromov M., Chopping Riemannian manifolds, in : Differential Geometry, Pitman Monographs Surveys Pure Appl. Math., Vol. 52, Longman Sci. Tech., Harlow, 1991, pp. 85-94. Zbl0722.53045MR93k:53034
  7. [7] Cheeger J., Gromov M., Taylor M., Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geom. 17 (1982) 15-53. Zbl0493.53035MR84b:58109
  8. [8] Greene R., Complete metrics of bounded curvature on noncompact manifolds, Arch. Math. 31 (1978) 89-95. Zbl0373.53018MR81h:53035
  9. [9] Greene R., Petersen P., Zhu S., Riemannian manifolds of faster-than-quadratic curvature decay, Internat. Math. Res. Notices 9 (1994) 363-377. Zbl0833.53037MR95m:53054
  10. [10] Gromov M., Volume and bounded cohomology, Publ. Math. IHES 56 (1982) 5-99. Zbl0516.53046MR84h:53053
  11. [11] Sha J., Shen Z., Complete manifolds with nonnegative Ricci curvature and quadratically nonnegatively curved infinity, Amer. J. Math. 119 (1997) 1399-1404. Zbl0901.53023MR99a:53046
  12. [12] Soma T., The Gromov volume of links, Invent. Math. 64 (1981) 445-454. Zbl0478.57006MR83a:57014

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