Skip Navigation



International Mathematics Research Notices Advance Access published online on August 5, 2009
International Mathematics Research Notices, doi:10.1093/imrn/rnp115
This Article
Right arrow Full Text
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Hakobyan, H.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oupjournals.org

Conformal Dimension: Cantor Sets and Fuglede Modulus

Hrant Hakobyan

Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4, Canada

Correspondence: Correspondence to be sent to: hhakob{at}math.toronto.edu

In this paper, we give several conditions for a space to be minimal for conformal dimension. We show that there are sets of zero length and conformal dimension 1, thus answering a question of Bishop and Tyson. Another sufficient condition for minimality is given in terms of a modulus of a system of measures in the sense of Fuglede [7]. It implies in particular that if Formula is minimal for conformal dimension and supports a measure {lambda} such that for every {varepsilon} > 0 there is a constant 0 < C < {infty} such that C–1 r1+{varepsilon} ≤ {lambda} (E{cap} B(x, r)) ≤ C r1–{varepsilon}, then X x Y is minimal for conformal dimension for every compact Y.

Communicated by Prof. Nikolai Makarov


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.