Falconer conjecture in the plane for random metrics

Details Falconer conjecture in the plane for random metrics Falconer conjecture in the plane for random metrics

2003-05-09

arxiv.org/abs/math/0305132v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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.

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