Valuations on convex sets, non-commutative determinants, and pluripotential theory

Abstract

A new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space $\HH^n$ is presented. In particular new examples of $Sp(n)Sp(1)$-invariant translation invariant continuous valuations are constructed. This method is based on the theory of plurisubharmonic functions of quaternionic variables.

39 pages. The definition of the quaternionic Hessian is replaced with the transposed matrix as it should be

Cited by in corpus (11)

• On quaternionic Monge-Ampere operator, closed positive currents and Lelong-Jensen type formula on quaternionic space
• Hessian valuations
• Classification of invariant valuations on the quaternionic plane
• Potential theory in several quaternionic variables
• Quaternionic Monge-Ampere equation and Calabi problem for HKT-manifolds
• Geometric valuation theory
• Quaternionic plurisubharmonic functions and their applications to convexity
• Theory of valuations on manifolds: a survey
• Local tensor valuations
• A Hadwiger-type theorem for the special unitary group
• Plurisubharmonic functions on the octonionic plane and Spin(9)-invariant valuations on convex sets