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Transactions of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9947-98-02317-4
MathSciNet review: 1608281
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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.


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  • [BW] 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. CMP 98:01
  • [E+] D.B.A. Epstein, J. Cannon, D.F. Holt, S. Levy, M.S. Paterson and W.P. Thurston, Word Processing in Groups, Jones and Bartlett, Boston, MA, 1992. MR 93i:20036
  • [EF] A. Eskin and B. Farb, Quasi-flats and rigidity in higher rank symmetric spaces, J. Amer. Math. Soc. 10 (1997), 653-692. CMP 97:11
  • [Ge1] S.M. Gersten, Quadratic divergence of geodesics in $CAT(0)$ spaces, Geometric and Functional Analysis, 4 (1994), 37-51. MR 95h:53057
  • [Ge2] S. Gersten, Quasi-isometry invariance of cohomological dimension, Comptes Rendues Acad. Sci. Paris, Ser. I Math. 316 (1993), 411-416. MR 94b:20042
  • [Gr] M. Gromov, Asymptotic Invariants of Infinite Groups, Geometric Group Theory, G. Niblo and M. Roller, eds., LMS Lecture Notes 182, Cambridge Univ. Press, 1993, pp. 1-295. MR 95m:20041
  • [KL] B. Kleiner and B. Leeb, Rigidity of quasi-isometries for symmetric spaces of higher rank, to appear in Publ. Math. IHES.

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Additional Information

Noel Brady
Affiliation: Department of Mathematics, Cornell University Ithaca, New York 14853
Email: brady@math.cornell.edu

Benson Farb
Affiliation: Department of Mathematics, University of Chicago 5734 University Ave. Chicago, Illinois 60637
Email: farb@math.uchicago.edu

DOI: https://doi.org/10.1090/S0002-9947-98-02317-4
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

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