Falconer conjecture in the plane for random metrics
Classical Analysis and ODEs
2007-05-23 v1 Combinatorics
Abstract
We prove the following variant of the Falconer conjecture in the plane. If the dimension of a compact planar set is greater than one, then the distance set with respect to almost every ellipse has positive Lebesgue measure.
Cite
@article{arxiv.math/0305132,
title = {Falconer conjecture in the plane for random metrics},
author = {S. Hofmann and A. Iosevich},
journal= {arXiv preprint arXiv:math/0305132},
year = {2007}
}