6 papers
Explicit solutions to Christoffel-Minkowski problems and Hessian equations under rotational symmetries
Fabian Mussnig, Jacopo Ulivelli
An explicit solution to the Christoffel-Minkowski problem for convex bodies of revolution is presented. The conditions on the prescribed measure involve only first moments over sph…
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…
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 inequalit…
Kubota-type formulas and supports of mixed measures
Daniel Hug, Fabian Mussnig, Jacopo Ulivelli
Kubota's integral formula expresses the intrinsic volumes of a convex body as averages over its projections onto linear subspaces. In this work, we introduce a new class of Kubota-…
Higher-Order Reverse Isoperimetric Inequalities for Log-concave Functions
Dylan Langharst, Francisco MarÃn Sola, Jacopo Ulivelli
The Rogers-Shephard and Zhang's projection inequalities are two reverse, affine isoperimetric-type inequalities for convex bodies. Following a classical work by Schneider, both ine…
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…