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Circular averages and Falconer/Erdös distance conjecture in the plane for random metrics
Author(s):
S.
Hofmann;
A.
Iosevich
Journal:
Proc. Amer. Math. Soc.
133
(2005),
133-143.
MSC (2000):
Primary 42B10, 52C10
Posted:
July 22, 2004
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Abstract:
We study a variant of the Falconer distance problem for perturbations of the Euclidean and related metrics. We prove that Mattila's criterion, expressed in terms of circular averages, which would imply the Falconer conjecture, holds on average. We also use a technique involving diophantine approximation to prove that the well-distributed case of the Erdös Distance Conjecture holds for almost every appropriate perturbation of the Euclidean metric.
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Additional Information:
S.
Hofmann
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email:
hofmann@math.missouri.edu
A.
Iosevich
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email:
iosevich@math.missouri.edu
DOI:
10.1090/S0002-9939-04-07603-8
PII:
S 0002-9939(04)07603-8
Received by editor(s):
July 19, 2003
Received by editor(s) in revised form:
September 8, 2003
Posted:
July 22, 2004
Additional Notes:
The research of the authors was partially supported by NSF grants
Communicated by:
Andreas Seeger
Copyright of article:
Copyright
2004,
American Mathematical Society
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