We introduce functional generalizations of the classical Cauchy-Kubota formulas for convex functions of n variables. We will show how such formulas follow from a functional Hadwiger theorem and how improved formulas can be obtained by using properties of mixed Monge-Ampère measures. The underlying setting connects to convex bodies in n-dimensional as well as (n+1)-dimensional space. If time permits, we will also discuss applications, such as functional versions of the additive kinematic formulas or questions on the supports of special mixed Monge-Ampère measures.

Based on joint works with Andrea Colesanti and Monika Ludwig as well as Daniel Hug and Jacopo Ulivelli.

PRIORITY:1 CLASS:PUBLIC BEGIN:VALARM TRIGGER:-