Falconer conjecture in the plane for random metrics

2003/05/09 by S. Hofmann, Hofmann, S., A. Iosevich +1
Mathematics · #42B #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #math.CA #math.CO #msc:42B

paper · pdf · doi:10.48550/arxiv.math/0305132

arxiv created 2003/05/09 · arxiv updated 2009/11/30

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.

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