Sharp stability of Brunn–Minkowski for homothetic regions
Peter van Hintum
University of Cambridge, UKHunter Spink
Harvard University, Cambridge, USAMarius Tiba
University of Cambridge, UK
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Abstract
We prove a sharp stability result concerning how close homothetic sets attaining near-equality in the Brunn–Minkowski inequality are to being convex. In particular, resolving a conjecture of Figalli and Jerison, we show there are universal constants such that for of positive measure, if , then for the convex hull of .
Cite this article
Peter van Hintum, Hunter Spink, Marius Tiba, Sharp stability of Brunn–Minkowski for homothetic regions. J. Eur. Math. Soc. 24 (2022), no. 12, pp. 4207–4223
DOI 10.4171/JEMS/1185