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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

An estimate for the volume entropy of nonpositively curved graph-manifolds


Author: S. Buyalo
Translated by: the author
Original publication: Algebra i Analiz, tom 15 (2003), nomer 1.
Journal: St. Petersburg Math. J. 15 (2004), 41-47
MSC (2000): Primary 53C22
Published electronically: December 31, 2003
MathSciNet review: 1979717
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $M$ be a closed 3-dimensional graph-manifold. It is proved that $h(g)>1$ for every geometrization $g$ of $M$, where $h(g)$ is the topological entropy of the geodesic flow of $g$.


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Additional Information

S. Buyalo
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191011, Russia
Email: buyalo@pdmi.ras.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-03-00801-X
PII: S 1061-0022(03)00801-X
Keywords: Volume entropy, graph-manifold, metrics of nonpositive curvature
Received by editor(s): September 2, 2002
Published electronically: December 31, 2003
Additional Notes: Partially supported by RFBR (grants nos. 02-01-00090 and 00-15-96024) and by CRDF (grant. no. RM1-2381-ST-02).
Article copyright: © Copyright 2003 American Mathematical Society