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