Sharp stability of Brunn–Minkowski for homothetic regions
Peter van HintumUniversity of Cambridge, UK
Hunter SpinkHarvard University, Cambridge, USA
Marius TibaUniversity of Cambridge, UK
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. 4207–4223DOI 10.4171/JEMS/1185