Plurisubharmonic functions on the octonionic plane and Spin(9)-invariant valuations on convex sets

Abstract

A new class of plurisubharmonic functions on the octonionic plane O^2= R^{16} is introduced. An octonionic version of theorems of A.D. Aleksandrov and Chern- Levine-Nirenberg, and Blocki are proved. These results are used to construct new examples of continuous translation invariant valuations on convex subsets of O^2=R^{16}. In particular a new example of Spin(9)-invariant valuation on R^{16} is given.

35 pages. The definition of octonionic Hessian is replaced with the transposed matrix as it should be. Other minor corrections

References in corpus (4)

• Valuations on convex sets, non-commutative determinants, and pluripotential theory
• Plurisubharmonic Functions in Calibrated Geometries
• A product formula for valuations on manifolds with applications to the integral geometry of the quaternionic line
• Quaternionic plurisubharmonic functions and their applications to convexity