Circular Averages and Falconer/erdos Distance Conjecture in the Plane for Random Metrics
نویسنده
چکیده
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 diophantine conversion mechanism to prove that well-distributed case of the Erdos Distance Conjecture holds for almost every appropriate perturbation of the Euclidean metric.
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