On a theorem of Schoen and Shkredov on sumsets of convex sets

Abstract

A set of reals $A=\{a_1,...,a_n\}$ labeled in increasing order is called convex if there exists a continuous strictly convex function $f$ such that $f(i)=a_i$ for every $i$. Given a convex set $A$, we prove \[|A+A|\gg\frac{|A|^{14/9}}{(\log|A|)^{2/9}}.\] Sumsets of different summands and an application to a sum-product-type problem are also studied either as remarks or as theorems.

References in corpus (2)

• Simple Proofs of Classical Theorems in Discrete Geometry via the Guth--Katz Polynomial Partitioning Technique
• Multi-fold sums from a set with few products

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