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Even $\mathrm{SO}(n)$ Equivariant Minkowski Valuations -- An Update Schuster, Franz

Description

To this day, the starting point for many important developments in valuation theory is Hadwiger's remarkable characterization of continuous rigid motion invariant real valued valuations as linear combinations of the intrinsic volumes. A fascinating open problem, dating back to work of R. Schneider from 1974, is the characterization of continuous {\it convex body valued} valuations which intertwine rigid motions. In this talk, we present some of the recent progress regarding this question. In particular, we discuss three different ways to represent an even such valuation, namely via Crofton measures, Klain bodies, and generating functions.

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