Calculus of Variations and Geometric Measure Theory
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A. Figalli - D. Jerison

A sharp Freiman type estimate for semisums in two and three dimensional Euclidean spaces

created by figalli on 19 Jul 2019

[BibTeX]

Accepted Paper

Inserted: 19 jul 2019
Last Updated: 19 jul 2019

Journal: Ann. Sci. Éc. Norm. Supér.
Year: 2019

Abstract:

Freiman's Theorem is a classical result in additive combinatorics concerning the approximate structure of sets of integers that contain a high proportion of their internal sums. As a consequence, one can deduce an estimate for sets of real numbers: ''If $A\subset \mathbb R$ and $
\frac12(A+A)
-
A
\ll
A
$, then $A$ is close to its convex hull.'' In this paper we prove a sharp form of the analogous result in dimensions 2 and 3.


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