7 citations · 15 across the 14 of their papers we have counts for
14 papers
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 inequality…
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…
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…
Polynomial valuations on convex functions and their maximal extensions
Jonas Knoerr, Jacopo Ulivelli
Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extensi…
Additive kinematic formulas for convex functions
Daniel Hug, Fabian Mussnig, Jacopo Ulivelli
We prove a functional version of the additive kinematic formula as an application of the Hadwiger theorem on convex functions together with a Kubota-type formula for mixed Monge-Am…
Higher-Order Reverse Isoperimetric Inequalities for Log-concave Functions
Dylan Langharst, Francisco Marín 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…
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-…
First variation of functional Wulff shapes
Jacopo Ulivelli
We introduce functional Wulff shapes based on the classical construction for compact convex sets. With this new tool, we establish a functional version of Aleksandrov's variational…
Entire Monge-Ampère equations and weighted Minkowski problems
Jacopo Ulivelli
In this short note, we prove the existence of solutions to a Monge-Ampère equation of entire type derived by a weighted version of the classical Minkowski problem.
The (Self-Similar, Variational) Rolling Stones
Dylan Langharst, Jacopo Ulivelli
The interplay between variational functionals and the Brunn-Minkowski Theory is a well-established phenomenon widely investigated in the last thirty years. In this work, we prove t…
From valuations on convex bodies to convex functions
Jonas Knoerr, Jacopo Ulivelli
A geometric framework relating valuations on convex bodies to valuations on convex functions is introduced. It is shown that a classical result by McMullen can be used to obtain a…
Convergence properties of symmetrization processes
Jacopo Ulivelli
Steiner symmetrization is well known for its rounding and general convergence properties. We identify a whole family of symmetrizations sharing analogue behaviors: In fact we prove…
Generalization of Klain's Theorem to Minkowski Symmetrization of compact sets and related topics
Jacopo Ulivelli
We shall prove a convergence result relative to sequences of Minkowski symmetrals of general compact sets. In particular, we investigate the case when this process is induced by se…