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math.MG2023
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…
math.MG2023
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…