Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Filling-invariants at infinity for manifolds of nonpositive curvature

Authors: Noel Brady and Benson Farb
Journal: Trans. Amer. Math. Soc. 350 (1998), 3393-3405
MSC (1991): Primary 53C23, 20F32, 57M07
MathSciNet review: 1608281
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we construct and study isoperimetric functions at infinity for Hadamard manifolds. These quasi-isometry invariants give a measure of the spread of geodesics in such a manifold.

References [Enhancements On Off] (What's this?)

  • J. Block and S. Weinberger, Large scale homology theories and geometry, Geometric Topology (Athens, GA, 1993), AMS/IP Stud. Adv. Math., vol. 2, part 1, Amer. Math. Soc., Providence, RI, 1997, pp. 522–569.
  • David B. A. Epstein, James W. Cannon, Derek F. Holt, Silvio V. F. Levy, Michael S. Paterson, and William P. Thurston, Word processing in groups, Jones and Bartlett Publishers, Boston, MA, 1992. MR 1161694
  • A. Eskin and B. Farb, Quasi-flats and rigidity in higher rank symmetric spaces, J. Amer. Math. Soc. 10 (1997), 653–692.
  • S. M. Gersten, Quadratic divergence of geodesics in ${\rm CAT}(0)$ spaces, Geom. Funct. Anal. 4 (1994), no. 1, 37–51. MR 1254309, DOI
  • Steve M. Gersten, Quasi-isometry invariance of cohomological dimension, C. R. Acad. Sci. Paris SΓ©r. I Math. 316 (1993), no. 5, 411–416 (English, with English and French summaries). MR 1209258
  • M. Gromov, Asymptotic invariants of infinite groups, Geometric group theory, Vol. 2 (Sussex, 1991) London Math. Soc. Lecture Note Ser., vol. 182, Cambridge Univ. Press, Cambridge, 1993, pp. 1–295. MR 1253544
  • B. Kleiner and B. Leeb, Rigidity of quasi-isometries for symmetric spaces of higher rank, to appear in Publ. Math. IHES.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 53C23, 20F32, 57M07

Retrieve articles in all journals with MSC (1991): 53C23, 20F32, 57M07

Additional Information

Noel Brady
Affiliation: Department of Mathematics, Cornell University Ithaca, New York 14853

Benson Farb
Affiliation: Department of Mathematics, University of Chicago 5734 University Ave. Chicago, Illinois 60637
MR Author ID: 329207

Received by editor(s): April 18, 1995
Received by editor(s) in revised form: October 25, 1996
Additional Notes: The second author is supported in part by an N.S.F. Postdoctoral Fellowship.
Article copyright: © Copyright 1998 American Mathematical Society