3 papers
math.MG2026
The sharp threshold for Hausdorff convexification under Minkowski addition
Peter van Hintum
The Dyn-Farkhi conjecture asserts that the square of the Hausdorff distance from a compact set to its convex hull is subadditive with respect to Minkowski addition. The conjecture…
math.CO2026
From Brunn-Minkowski to Prékopa-Leindler and Borell-Brascamp-Lieb: discrete inequalities
Peter van Hintum
We consider a general way to obtain Prékopa-Leindler and Borell-Brascamp-Lieb type inequalities from Brunn-Minkowski type inequalities and provide numerous examples. We use the sa…
math.FA2025
Sharp Quantitative Stability for the Prékopa-Leindler and Borell-Brascamp-Lieb Inequalities
Alessio Figalli, Peter van Hintum, Marius Tiba
The Borell-Brascamp-Lieb inequality is a classical extension of the Prékopa-Leindler inequality, which in turn is a functional counterpart of the Brunn-Minkowski inequality. The s…