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An estimate for the volume entropy of nonpositively curved graph-manifolds
Author(s):
S.
Buyalo
Translated by:
the author
Original publication:
Algebra i Analiz,
tom 15
(2003),
vypusk 1.
Journal:
St. Petersburg Math. J.
15
(2004),
41-47.
MSC (2000):
Primary 53C22
Posted:
December 31, 2003
MathSciNet review:
1979717
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References |
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Abstract:
Let  be a closed 3-dimensional graph-manifold. It is proved that  for every geometrization  of  , where  is the topological entropy of the geodesic flow of  .
References:
-
- [BW]
- W. Ballmann and M. Wojtkowski, An estimate for the measure-theoretic entropy of geodesic flows, Ergodic Theory Dynam. Systems 9 (1989), 271-279. MR 90k:58165
- [BK]
- S. V. Buyalo and V. L. Kobel'skii, Geometrization of graph-manifolds. II. Isometric geometrization, Algebra i Analiz 7 (1995), no. 3, 96-117; English transl., St. Petersburg Math. J. 7 (1996), no. 3, 387-404. MR 97k:57017
- [BS]
- S. Buyalo and V. Schroeder, On the asymptotic geometry of nonpositively curved graphmanifolds, Trans. Amer. Math. Soc. 353 (2001), 853-875. MR 2001f:53063
- [CK]
- C. Croke and B. Kleiner, The geodesic flow and a nonpositively curved graph manifold, arXiv:math. DG/9911170, 1999.
- [HS]
- C. Hummel and V. Schroeder, Tits geometry of cocompact real-analytic Hadamard manifolds of dimension 4, Differential Geom. Appl. 11 (1999), 129-143. MR 2000h:53052
- [L]
- B. Leeb, 3-manifolds with(out) metrics of nonpositive curvature, Invent. Math. 122 (1995), 277-289. MR 97g:57015
- [M]
- Manning A., Topological entropy for geodesic flows, Ann. of Math. (2) 110 (1979), 567-573. MR 81e:58044
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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:
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):
2/SEP/2002
Posted:
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).
Copyright of article:
Copyright
2003,
American Mathematical Society
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