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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: 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.

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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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