Abstract
For any compact set K⊂RN we construct a hyperbolic graph C K , such that the conformal dimension of C K is at most the box dimension of K.
Similar content being viewed by others
References
Ballmann, W.: Lectures on Spaces of Nonpositive Curvature, DMV Sem. 25, Birkhauser, Basel, 1995.
Brick, S.: Quasi-isometries and ends of groups, J. Pure Appl. Algebra 86 (1993), 23-33.
Gromov, M.: Geometric group theory, in: Asymptotic Invariants of Infinite Groups (Brighton 1991), Vol. II, London Math. Soc. Lecture Note Ser. 182, Cambridge Univ. Press, 1993.
Gromov, M.: Hyperbolic groups, in: Essays in Group Theory, Math. Sci. Res. Inst. Publ. 8, Springer, New York, 1987, pp. 75-263.
Murphy, G.: C -algebras and Operator Theory, Academic Press, 1990.
Roe, J.: Coarse cohomology and index theory on complete Riemannian manifolds, Mem. Amer. Math. Soc. 104(497) (1993).
Roe, J.: Hyperbolic metric spaces and the exotic cohomology Novikov conjecture, K-Theory 4 (1990), 501-512.
Pansu, P.: Cohomologie Lp des variétés à courbure negative, cas du degre 1., Rend. Sem. Mat. Univ. Politec. Torino (1989), 95-120.
Tricot, C.: Two definitions of fractional dimension, Math. Proc. Camb. Philos. Soc. 91 (1982), 57-74.
Rights and permissions
About this article
Cite this article
Elek, G. The l p -Cohomology and the Conformal Dimension of Hyperbolic Cones. Geometriae Dedicata 68, 263–279 (1997). https://doi.org/10.1023/A:1004920322337
Issue Date:
DOI: https://doi.org/10.1023/A:1004920322337