University of Cambridge > > Partial Differential Equations seminar > Stability results for the semisum of sets in R^n

Stability results for the semisum of sets in R^n

Add to your list(s) Download to your calendar using vCal

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 Partial Differential Equations seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2022, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity