The sharp doubling threshold for approximate convexity
Copyright policy )The sharp doubling threshold for approximate convexity
AbstractWe show for of equal volume and that if , then (up to translation) is bounded. This establishes the sharp threshold for the quantitative stability of the Brunn–Minkowski inequality recently established by Figalli, van Hintum, and Tiba, the proof of which uses our current result. We additionally establish a similar sharp threshold for iterated sumsets.
- University of Oxford United Kingdom
- New College University of Oxford United Kingdom
- UNIVERSITY OF OXFORD
- UNIVERSITY OF OXFORD
- UNIVERSITY OF OXFORD
Optimal transportation, Inverse problems of additive number theory, including sumsets, quantitative stability, Metric Geometry (math.MG), iterated sumsets, Brunn-Minkowski inequality, Mathematics - Metric Geometry, 11P70, 52A40, 49Q20, 49Q22, Inequalities and extremum problems involving convexity in convex geometry, Variational problems in a geometric measure-theoretic setting, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), sharp doubling threshold, convex hull
Optimal transportation, Inverse problems of additive number theory, including sumsets, quantitative stability, Metric Geometry (math.MG), iterated sumsets, Brunn-Minkowski inequality, Mathematics - Metric Geometry, 11P70, 52A40, 49Q20, 49Q22, Inequalities and extremum problems involving convexity in convex geometry, Variational problems in a geometric measure-theoretic setting, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), sharp doubling threshold, convex hull
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