Low dimensional pinned distance sets via spherical averages

Published 29 Jan 2021 in math.CA | (2101.12589v2)

Abstract: An inequality is derived for the average $t$-energy of pinned distance measures, where $0 < t < 1$. This refines Mattila's theorem on distance sets to pinned distance sets, and gives an analogue of Liu's theorem for pinned distance sets of dimension smaller than 1.

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Terence L. J. Harris

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