Constructs counterexamples showing the symmetric Dyn-Farkhi conjecture fails for n≥3 and proves that the n-fold Minkowski average is the sharp threshold for a guaranteed drop in Hausdorff distance to the convex hull.
Sharp quantitative stability of the Brunn-Minkowski inequality
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The sharp threshold for Hausdorff convexification under Minkowski addition
Constructs counterexamples showing the symmetric Dyn-Farkhi conjecture fails for n≥3 and proves that the n-fold Minkowski average is the sharp threshold for a guaranteed drop in Hausdorff distance to the convex hull.