Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Sets of minimal Hausdorff dimension for quasiconformal maps

Author: Jeremy T. Tyson
Journal: Proc. Amer. Math. Soc. 128 (2000), 3361-3367
MSC (2000): Primary 30C65; Secondary 28A78
Published electronically: May 18, 2000
MathSciNet review: 1676353
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For any $1\le\alpha\le n$, there is a compact set $E\subset\mathbb{R}^n$ of (Hausdorff) dimension $\alpha$ whose dimension cannot be lowered by any quasiconformal map $f:\mathbb{R}^n\to\mathbb{R}^n$. We conjecture that no such set exists in the case $\alpha<1$. More generally, we identify a broad class of metric spaces whose Hausdorff dimension is minimal among quasisymmetric images.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 30C65, 28A78

Retrieve articles in all journals with MSC (2000): 30C65, 28A78

Additional Information

Jeremy T. Tyson
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Address at time of publication: Department of Mathematics, State University of New York at Stony Brook, Stony Brook, New York 11794-3651

Keywords: Hausdorff dimension, quasiconformal maps, generalized modulus
Received by editor(s): October 15, 1998
Received by editor(s) in revised form: January 15, 1999
Published electronically: May 18, 2000
Additional Notes: The results of this paper form part of the author’s doctoral dissertation at the University of Michigan. The author was supported by a National Science Foundation Graduate Research Fellowship and a Sloan Doctoral Dissertation Fellowship.
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2000 American Mathematical Society