The Brunn – Minkowski theorem and related geometric and functional inequalities

  title={The Brunn – Minkowski theorem and related geometric and functional inequalities},
  author={F. Barthe},
The Brunn–Minkowski inequality gives a lower bound of the Lebesgue measure of a sum-set in terms of the measures of the individual sets. It has played a crucial role in the theory of convex bodies. This topic has many interactions with isoperimetry or functional analysis. Our aim here is to report some recent aspects of these interactions involving optimal mass transport or the Heat equation. Among other things, we will present Brunn–Minkowski inequalities for flat sets, or in Gauss space, as… CONTINUE READING


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