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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



An upper bound for the curvature integral

Author: 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
Published electronically: January 30, 2009
MathSciNet review: 2423998
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Abstract | References | Similar Articles | 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 [Enhancements On Off] (What's this?)

  • [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

Keywords: Sectional curvature, scalar curvature, Aleksandrov space
Received by editor(s): April 5, 2007
Published electronically: January 30, 2009
Article copyright: © Copyright 2009 American Mathematical Society

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