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University of Cambridge > Talks.cam > Geometric Analysis and Partial Differential Equations seminar > Stability results for the semisum of sets in R^n

## Stability results for the semisum of sets in R^nAdd to your list(s) Download to your calendar using vCal - Alessio Figalli
- Monday 19 May 2014, 15:00-16:00
- CMS, MR13.
If you have a question about this talk, please contact D.Goldman. Given a Borel A in R^n of positive measure, one can consider its semisum S=(A+A)/2. It is clear that S contains A, and it is not difficult to prove that they have the same measure if and only if A is equal to his convex hull minus a set of measure zero. We now wonder whether this statement is stable: if the measure of S is close to the one of A, is A close to his convex hull? More generally, one may consider the semisum of two different sets A and B, in which case our question corresponds to proving a stability result for the Brunn-Minkowski inequality. When n=1, one can approximate a set with finite unions of intervals to translate the problem to the integers Z. In this discrete setting the question becomes a well-studied problem in additive combinatorics, usually known as Freiman’s Theorem. In this talk I will review some results in the one-dimensional discrete setting and describe how to answer to the problem in arbitrary dimension. This talk is part of the Geometric Analysis and Partial Differential Equations seminar series. ## This talk is included in these lists:- All CMS events
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