3 papers
math.FA2026
A strengthening of the dimensional Brunn-Minkowski conjecture implies the (B)-conjecture
Sotiris Armeniakos, Jacopo Ulivelli
We prove that if a sufficiently regular even log-concave measure satisfies a certain stronger form of the dimensional Brunn-Minkowski conjecture, then it also satisfies the (B)-con…
math.FA2026
A new infinitesimal form of the Prékopa-Leindler inequality with multiplicative structure and applications
Sotiris Armeniakos, Jacopo Ulivelli
By differentiating a concavity principle arising from the Prékopa-Leindler inequality, we obtain a statement simultaneously strengthening the weighted boundary Poincaré inequality…
math.FA2024
Inequalities and counterexamples for functional intrinsic volumes and beyond
Fabian Mussnig, Jacopo Ulivelli
We show that analytic analogs of Brunn-Minkowski-type inequalities fail for functional intrinsic volumes on convex functions. This is demonstrated both through counterexamples and…