Quantitative stability for the Brunn–Minkowski inequality
Copyright policy )Quantitative stability for the Brunn–Minkowski inequality
We prove a quantitative stability result for the Brunn-Minkowski inequality: if $|A|=|B|=1$, $t \in [τ,1-τ]$ with $τ>0$, and $|tA+(1-t)B|^{1/n}\leq 1+δ$ for some small $δ$, then, up to a translation, both $A$ and $B$ are quantitatively close (in terms of $δ$) to a convex set $K$.
- Massachusetts instute of technology EAPS United States
- ETH Zurich Switzerland
- The University of Texas at Austin United States
- Massachusetts Institute of Technology Dept. of Economics United States
- Massachusetts Institute of Technology United States
Mathematics - Functional Analysis, Mathematics - Metric Geometry, quantitative stability, Inequalities and extremum problems involving convexity in convex geometry, FOS: Mathematics, Metric Geometry (math.MG), Brunn-Minkowski inequality, Functional Analysis (math.FA)
Mathematics - Functional Analysis, Mathematics - Metric Geometry, quantitative stability, Inequalities and extremum problems involving convexity in convex geometry, FOS: Mathematics, Metric Geometry (math.MG), Brunn-Minkowski inequality, Functional Analysis (math.FA)
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