Ensembles de petite somme, structure de sous-criticité

Abstract

In 1991, Ruzsa proved a precise lower bound for the measure of the sum of two bounded sets of real numbers A and B involving the ratio λ(A)/λ(B) and the diameter of B. The structure of critical sets for this lower bound was described by Roton in 2018. In this paper, we describe the structure of nearly critical sets for Ruzsa’s inequality.

Locations

• Journal de Théorie des Nombres de Bordeaux - View - PDF
• arXiv (Cornell University) - View - PDF