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arXiv · 1207.5062

Near Equality in the Brunn-Minkowski Inequality

Michael Christ
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Abstract

A pair of subsets of Euclidean space which nearly achieves equality in the Brunn-Minkowski inequality must nearly coincide with a pair of homothetic convex sets. The two-dimensional case was treated in a previous paper in this series by an argument which does not seem to generalize to higher dimensions. Here the result is extended to arbitrary dimensions. An induction on the dimension, a symmetrization argument, and a description of near solutions of an additive functional equation are used to establish sufficient regularity to set up a compactness argument.

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Michael Christ. 2012-07-20. Near Equality in the Brunn-Minkowski Inequality. https://arxiv.org/abs/1207.5062

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