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Search: MSC category 11B99 ( None of the above, but in this section )

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Schoen, Tomasz
On Convolutions of Convex Sets and Related Problems
We prove some results concerning covolutions, the additive energy and sumsets of convex sets and its generalizations. In particular, we show that if a set $A=\{a_1,\dots,a_n\}_\lt \subseteq \mathbb R$ has the property that for every fixed $1\leqslant d\lt n,$ all differences $a_i-a_{i-d}$, $d\lt i\lt n,$ are distinct, then $|A+A|\gg |A|^{3/2+c}$ for a constant $c\gt 0.$

Keywords:convex sets, additive energy, sumsets
Category:11B99

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