Distance graphs and sets of positive upper density in ℝd

Neil Lyall, Ákos Magyar

Type: Article

Publication Date: 2020-04-15

Citations: 15

DOI: https://doi.org/10.2140/apde.2020.13.685

Abstract

We present a sharp extension of a result of Bourgain on finding configurations of k + 1 points in general position in measurable subset of R d of positive upper density whenever d ≥ k + 1 to all proper k-degenerate distance graphs.

Locations

Analysis & PDE - View
arXiv (Cornell University) - View - PDF
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