Sets of minimal Hausdorff dimension for quasiconformal maps
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- by Jeremy T. Tyson PDF
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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
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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
- MR Author ID: 625886
- Email: jttyson@math.lsa.umich.edu, tyson@math.sunysb.edu
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3361-3367
- MSC (2000): Primary 30C65; Secondary 28A78
- DOI: https://doi.org/10.1090/S0002-9939-00-05433-2
- MathSciNet review: 1676353