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Sets of minimal Hausdorff dimension for quasiconformal maps
Author(s):
Jeremy
T.
Tyson
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3361-3367.
MSC (2000):
Primary 30C65;
Secondary 28A78
Posted:
May 18, 2000
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Abstract:
For any  , there is a compact set  of (Hausdorff) dimension  whose dimension cannot be lowered by any quasiconformal map  . We conjecture that no such set exists in the case  . More generally, we identify a broad class of metric spaces whose Hausdorff dimension is minimal among quasisymmetric images.
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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
Email:
jttyson@math.lsa.umich.edu, tyson@math.sunysb.edu
DOI:
10.1090/S0002-9939-00-05433-2
PII:
S 0002-9939(00)05433-2
Keywords:
Hausdorff dimension,
quasiconformal maps,
generalized modulus
Received by editor(s):
October 15, 1998
Received by editor(s) in revised form:
January 15, 1999
Posted:
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 of article:
Copyright
2000,
American Mathematical Society
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