Dmitry Tsarev

On the largest size of sum-free sets in symmetric regions

A subset $S$ of a group $G$ is said to be sum-free (resp. $\Delta$-free) if there are no solutions to $a+b=c$ (resp. $a+b+c=0$) with $a,b,c\in S$. For a convex region $R\subset\mathbb{R}^d$, let $\sigma(R)$ denote the maximal proportion of the volume of $R$ that a sum-free subset of $R$ can occupy. We prove that $\sigm...