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

Buyalo, S.

doi:10.1090/S1061-0022-03-00801-X

An estimate for the volume entropy of nonpositively curved graph-manifolds
HTML articles powered by AMS MathViewer

by S. Buyalo
Translated by: the author

St. Petersburg Math. J. 15 (2004), 41-47

DOI: https://doi.org/10.1090/S1061-0022-03-00801-X

Published electronically: December 31, 2003

PDF | Request permission

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 $g$.

References

John W. Green, Harmonic functions in domains with multiple boundary points, Amer. J. Math. 61 (1939), 609–632. MR 90, DOI 10.2307/2371316
J. C. Oxtoby and S. M. Ulam, On the existence of a measure invariant under a transformation, Ann. of Math. (2) 40 (1939), 560–566. MR 97, DOI 10.2307/1968940
S. Losinsky, Sur le procédé d’interpolation de Fejér, C. R. (Doklady) Acad. Sci. URSS (N.S.) 24 (1939), 318–321 (French). MR 0002001
C. Croke and B. Kleiner, The geodesic flow and a nonpositively curved graph manifold, arXiv:math. DG/9911170, 1999.
P. Erdös, On the distribution of normal point groups, Proc. Nat. Acad. Sci. U.S.A. 26 (1940), 294–297. MR 2000, DOI 10.1073/pnas.26.4.294
J. C. Oxtoby and S. M. Ulam, On the existence of a measure invariant under a transformation, Ann. of Math. (2) 40 (1939), 560–566. MR 97, DOI 10.2307/1968940
I. M. Sheffer, Some properties of polynomial sets of type zero, Duke Math. J. 5 (1939), 590–622. MR 81