On sums of Szemerédi--Trotter sets

Abstract

We prove new general results on sumsets of sets having Szemerédi--Trotter type. This family includes convex sets, sets with small multiplicative doubling, images of sets under convex/concave maps and others.

12 pages

References in corpus (1)

• Some new inequalities in additive combinatorics

Cited by in corpus (3)

• On sum sets of convex functions
• On the number of unit-area triangles spanned by convex grids in the plane
• On multiplicative properties of combinatorial cubes