Minkowski valuations in a 2-dimensional complex vector space

Abstract

The classification of continuous, translation invariant Minkowski valuations which are contravariant (or covariant) with respect to the complex special linear group is established in a 2-dimensional complex vector space. Every such valuation is given by the sum of a valuation of degree of homogeneity 1 and 3. In dimensions $m\ge 3$ such a classification was previously established and only valuations of a degree of homogeneity 2m-1 appear.

9 pages

References in corpus (3)

• Crofton measures and Minkowski valuations
• Complex Intersection Bodies
• On the inverse Klain map

Cited by in corpus (1)

• $L_p$ Minkowski Valuations on polytopes