Geodesic
On sums of Szemer\'edi--Trotter sets
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected issues of mathematics and mechanics, Tome 289 (2015), pp. 318-327

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We prove new general results on sumsets and difference sets for sets of the Szemerédi–Trotter type. This family includes convex sets, sets with small multiplicative doubling, images of sets under convex/concave maps and others. 
@article{TM_2015_289_a17,
     author = {I. D. Shkredov},
     title = {On sums of {Szemer\'edi--Trotter} sets},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {318--327},
     publisher = {mathdoc},
     volume = {289},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2015_289_a17/}
}
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I. D. Shkredov. On sums of Szemer\'edi--Trotter sets. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected issues of mathematics and mechanics, Tome 289 (2015), pp. 318-327. http://geodesic.mathdoc.fr/item/TM_2015_289_a17/