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

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

2004-01-19

arxiv.org/abs/math/0401219v4

Adv. Math. 195 (2005), no. 2, 561--595.

Mathematics

Metric Geometry

39 pages, minor corrections

Scientific paper

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.

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