Abstract
We formulate and prove a foliated version of a theorem of Besson, Courtois, and Gallot establishing the minimal entropy rigidity of negatively curved locally symmetric spaces. One corollary is a foliated version of Mostow’s rigidity theorem.
Similar content being viewed by others
References
G. Besson, G. Courtois and S. Gallot,Entropies et rigidités des espaces localement symétriques de courbure strictement négative, Geometric and Functional Analysis5 (1995), 731–799.
G. Besson, G. Courtois and S. Gallot,Minimal entropy and mostow’s rigidity theorems, Ergodic Theory and Dynamical Systems16 (1996), 623–649.
A. L. Besse,Einstein Manifolds, Springer-Verlag, Berlin, 1987.
A. Connes,Noncommutative Geometry, Academic Press Inc., San Diego, CA, 1994.
P. Eberlein,Geometry of nonpositively curved manifolds, Chicago Lectures in Mathematics, University of Chicago Press, 1996.
F. T. Farrell and L. E. Jones,Topological rigidity for compact non-positively curved manifolds, inDifferential Geometry: Riemannian Geometry (Los Angeles, CA, 1990), American Mathematical Society, Providence, RI, 1993, pp. 229–274.
J. Feldman and C. C. Moore,Ergodic equivalence relations, cohomology, and von Neumann algebras. I, Bulletin of the American Mathematical Society81 (1975), 921–924.
S. Hurder,Coarse geometry of foliations, inGeometric Study of Foliations (Tokyo, 1993), World Science Publishing, River Edge, NJ, 1994, pp. 35–96.
A. Manning,Topological entropy for geodesic flows, Annals of Mathematics (2)110 (1979), 567–573.
Y. N. Minsky,On rigidity, limit sets, and end invariants of hyperbolic 3-manifolds, Journal of the American Mathematical Society7 (1994), 539–588.
S. J. Patterson,The limit set of a Fuchsian group, Acta Mathematica136 (1976), 241–273.
P. Pansu and R. Zimmer,Rigidity of locally homogeneous metrics of negative curvature on the leaves of a foliation, Israel Journal of Mathematics68 (1989), 56–62.
D. Sullivan,The density at infinity of a discrete group of hyperbolic motions, Publications Mathématiques de l’Institut des Hautes Études Scientifiques50 (1979), 225–250.
R. J. Zimmer,Ergodic theory, semisimple Lie groups, and foliations by manifolds of negative curvature, Publications Mathématiques de l’Institut des Hautes Études Scientifiques55 (1982), 37–62.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Boland, J., Connell, C. Minimal entropy rigidity for foliations of compact spaces. Isr. J. Math. 128, 221–246 (2002). https://doi.org/10.1007/BF02785426
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02785426