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An upper bound for the curvature integral
Author(s):
A.
M.
Petrunin
Translated by:
the author
Original publication:
Algebra i Analiz,
tom 20
(2008),
nomer 2.
Journal:
St. Petersburg Math. J.
20
(2009),
255-265.
MSC (2000):
Primary 53B21
Posted:
January 30, 2009
MathSciNet review:
2423998
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Additional information
Abstract:
It is shown that the integral of the scalar curvature of a closed Riemannian manifold can be bounded from above in terms of the manifold's dimension, diameter, and a lower bound for the sectional curvature.
References:
-
- [BGP]
- Yu. D. Burago, M. L. Gromov, and G. Ya. Perel'man, A. D. Aleksandrov spaces with curvatures bounded below, Uspekhi Mat. Nauk 47 (1992), no. 2, 3-51; English transl., Russian Math. Surveys 47 (1992), no. 2, 1-58. MR 1185284 (93m:53035)
- [Buy]
- S. V. Buyalo, Some analytic properties of convex sets in Riemannian spaces, Mat. Sb. (N.S.) 107 ( 149) (1978), no. 1, 37-55; English transl. in Math. USSR-Sb. 35 (1978). MR 0510141 (80a:53071)
- [P-2003]
- A. Petrunin, Polyhedral approximations of Riemannian manifolds, Turkish J. Math. 27 (2003), no. 1, 173-187. MR 1975337 (2004f:53035)
- [P-2007]
- -, Semiconcave functions in Alexandrov's geometry, Surveys in Differential Geometry, vol. 11, Internat. Press, Somerville, MA, 2007, pp. 137-201. MR 2408266.
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Additional Information:
A.
M.
Petrunin
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
Email:
petrunin@math.psu.edu
DOI:
10.1090/S1061-0022-09-01046-2
PII:
S 1061-0022(09)01046-2
Keywords:
Sectional curvature,
scalar curvature,
Aleksandrov space
Received by editor(s):
5/APR/2007
Posted:
January 30, 2009
Copyright of article:
Copyright
2009,
American Mathematical Society
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