Skip to main content
Log in

The l p -Cohomology and the Conformal Dimension of Hyperbolic Cones

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Ballmann, W.: Lectures on Spaces of Nonpositive Curvature, DMV Sem. 25, Birkhauser, Basel, 1995.

    Google Scholar 

  2. Brick, S.: Quasi-isometries and ends of groups, J. Pure Appl. Algebra 86 (1993), 23-33.

    Google Scholar 

  3. 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.

  4. Gromov, M.: Hyperbolic groups, in: Essays in Group Theory, Math. Sci. Res. Inst. Publ. 8, Springer, New York, 1987, pp. 75-263.

    Google Scholar 

  5. Murphy, G.: C -algebras and Operator Theory, Academic Press, 1990.

  6. Roe, J.: Coarse cohomology and index theory on complete Riemannian manifolds, Mem. Amer. Math. Soc. 104(497) (1993).

  7. Roe, J.: Hyperbolic metric spaces and the exotic cohomology Novikov conjecture, K-Theory 4 (1990), 501-512.

    Google Scholar 

  8. Pansu, P.: Cohomologie Lp des variétés à courbure negative, cas du degre 1., Rend. Sem. Mat. Univ. Politec. Torino (1989), 95-120.

  9. Tricot, C.: Two definitions of fractional dimension, Math. Proc. Camb. Philos. Soc. 91 (1982), 57-74.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints 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

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1004920322337

Navigation