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math.MG2023
Smooth valuations on convex bodies and finite linear combinations of mixed volumes
Jonas Knoerr
It is shown that Alesker's solution of McMullen's conjecture implies the following stronger version of the conjecture: Every continuous, translation invariant, -homogeneous valu…
math.MG2023
Monge-Ampère operators and valuations
Jonas Knoerr
Two classes of measure-valued valuations on convex functions related to Monge-Ampère operators are investigated and classified. It is shown that the space of all valuations with va…
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…