Circular averages and Falconer/Erdös distance conjecture in the plane for random metrics
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- by S. Hofmann and A. Iosevich PDF
- Proc. Amer. Math. Soc. 133 (2005), 133-143 Request permission
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.References
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Additional Information
- S. Hofmann
- Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
- MR Author ID: 251819
- ORCID: 0000-0003-1110-6970
- Email: hofmann@math.missouri.edu
- A. Iosevich
- Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
- MR Author ID: 356191
- Email: iosevich@math.missouri.edu
- Received by editor(s): July 19, 2003
- Received by editor(s) in revised form: September 8, 2003
- Published electronically: July 22, 2004
- Additional Notes: The research of the authors was partially supported by NSF grants
- Communicated by: Andreas Seeger
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 133-143
- MSC (2000): Primary 42B10, 52C10
- DOI: https://doi.org/10.1090/S0002-9939-04-07603-8
- MathSciNet review: 2085162