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arxiv: math/0305132 · v1 · submitted 2003-05-09 · 🧮 math.CA · math.CO

Falconer conjecture in the plane for random metrics

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keywords conjecturefalconerplanealmostcompactdimensiondistanceellipse
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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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