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SUMMARY:Stability results for the semisum of sets in R^n - Alessio Figalli
  - UT Austin
DTSTART:20140519T140000Z
DTEND:20140519T150000Z
UID:TALK52736@talks.cam.ac.uk
CONTACT:37739
DESCRIPTION: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 diffi
 cult to prove\nthat they have the same measure if and only if A is equal t
 o his convex\nhull minus a set of measure zero. We now wonder whether this
  statement is stable: \nif the measure of S is close to the one of A\, is 
 A close to his convex hull? More generally\, one\nmay 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 th
 e problem to the integers Z. In this  discrete setting the question become
 s a well-studied problem in additive combinatorics\, usually known as Frei
 man's Theorem.\nIn this talk I will review some results in the one-dimensi
 onal discrete\nsetting and describe how to answer to the problem in arbitr
 ary dimension.
LOCATION:MR14
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