7 citations · 15 across the 14 of their papers we have counts for
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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…
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…
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…