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Large volume growth and finite topological type
Author(s):
D.
Ordway;
B.
Stephens;
D.
G.
Yang
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1191-1196.
MSC (1991):
Primary 53C21
Posted:
December 10, 1999
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Abstract:
It is shown in this paper that a complete noncompact  -dimensional Riemannian manifold with nonnegative Ricci curvature, sectional curvature bounded from below, and large volume growth is of finite topological type provided that the volume growth rate of the complement of the cone of rays from a fixed base point is less than  .
References:
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- J. Cheeger and D. Ebin, Comparison theorems in Riemannian geometry, North-Holland, Amsterdam (1975). MR 56:16538
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- Z. M. Shen and G.F. Wei, Volume growth and finite topological type, Differential geometry: Riemannian geometry (Los Angeles, CA, 1990), 539-549, Proc. Sympos. Pure Math., 54, Part 3, Amer. Math. Soc., Providence, RI, 1993. MR 94e:53036
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Additional Information:
D.
Ordway
Affiliation:
Department of Mathematics, Harvard University, Cambridge, Massachusetts 02139
Email:
ordway@abel.math.harvard.edu
B.
Stephens
Affiliation:
Department of Mathematics, Harvard University, Cambridge, Massachusetts 02139
Email:
bstephen@fas.harvard.edu
D.
G.
Yang
Affiliation:
Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
Email:
dgy@math.tulane.edu
DOI:
10.1090/S0002-9939-99-05609-9
PII:
S 0002-9939(99)05609-9
Keywords:
Excess function,
finite topological type,
large volume growth,
nonnegative Ricci curvature,
Riemannian manifold,
volume comparison theorem
Received by editor(s):
January 11, 1998
Posted:
December 10, 1999
Additional Notes:
This research was partially supported by NSF grant DMS97-32058.
Communicated by:
Christopher Croke
Copyright of article:
Copyright
2000,
American Mathematical Society
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