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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Volume entropy and integral Ricci curvatures over closed geodesics


Author: Seong-Hun Paeng
Journal: Proc. Amer. Math. Soc. 135 (2007), 3677-3684
MSC (2000): Primary 53C20; Secondary 53C23
Published electronically: May 2, 2007
MathSciNet review: 2336584
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Abstract: We obtain an upper bound of the volume entropy and the simplicial volume with integrals of Ricci curvature over closed geodesics and apply it to the real Schwarz lemma by Besson, Courtois and Gallot.


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Additional Information

Seong-Hun Paeng
Affiliation: Department of Mathematics, Konkuk University, 1 Hwayang-dong, Gwangjin-gu, Seoul 143-701, Korea
Email: shpaeng@konkuk.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08869-7
PII: S 0002-9939(07)08869-7
Keywords: Volume entropy, simplicial volume, integral Ricci curvature, hyperbolic manifold
Received by editor(s): July 20, 2006
Received by editor(s) in revised form: August 7, 2006
Published electronically: May 2, 2007
Additional Notes: This work was supported by grant No. R01-2006-000-10047-0(2006) from the Basic Research Program of the Korea Science $&$ Engineering Foundation.
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2007 American Mathematical Society