Geodesic
Sharpening an Estimate of the Size
Matematičeskie zametki, Tome 107 (2020) no. 6, pp. 902-905

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A finite set $A=\{a_1\dotsb$ is said to be convex if the sequence $(a_i-a_{i-1})_{i=2}^n$ is strictly increasing. Using an estimate of the additive energy of convex sets, one can estimate the size of the sumset as $|A+A|\gtrsim|A|^{102/65}$, which slightly sharpens Shkredov's latest result $|A+A|\gtrsim|A|^{58/37}$.
Keywords: additive combinatorics, sumset, convex sets, convex sequences. 
@article{MZM_2020_107_6_a9,
     author = {K. I. Olmezov},
     title = {Sharpening an {Estimate} of the {Size}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {902--905},
     publisher = {mathdoc},
     volume = {107},
     number = {6},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_6_a9/}
}
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K. I. Olmezov. Sharpening an Estimate of the Size. Matematičeskie zametki, Tome 107 (2020) no. 6, pp. 902-905. http://geodesic.mathdoc.fr/item/MZM_2020_107_6_a9/