K-distance sets, Falconer conjecture, and discrete analogs

2003/03/18 by Alex Iosevich, A. Iosevich, Iosevich, A. +3
Mathematics · #42B99 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #math.CA #msc:42B99

paper · pdf · doi:10.48550/arxiv.math/0303227

10 pages

arxiv created 2003/03/18 · openalex publication_date 2003/03/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a series of results on the size of distance sets corresponding to sets in the Euclidean space. These distances are generated by bounded convex sets and the results depend explicitly on the geometry of these sets. We also use a diophantine mechanism to convert continuous results into distance set estimates for discrete point sets.

Citations

• Distance sets corresponding to convex bodies

Related

• On the distance sets spanned by sets of dimension d/2 in ℝ^d
• Theory of dimension for large discrete sets and applications
• On integer distance sets
• A generalization of Larman-Rogers-Seidel's theorem
• Endpoint bounds for the non-isotropic Falconer distance problem associated with lattice-like sets