Sharp quantitative stability of the planar Brunn–Minkowski inequality
Peter van Hintum
University of Cambridge, UKHunter Spink
Stanford University, USAMarius Tiba
University of Cambridge, UK
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Abstract
We prove a sharp stability result for the Brunn–Minkowski inequality for . Assuming that the Brunn–Minkowski deficit is sufficiently small in terms of , there exist homothetic convex sets and such that . The key ingredient is to show for every , if is sufficiently small then .
Cite this article
Peter van Hintum, Hunter Spink, Marius Tiba, Sharp quantitative stability of the planar Brunn–Minkowski inequality. J. Eur. Math. Soc. 26 (2024), no. 2, pp. 695–730
DOI 10.4171/JEMS/1372