Plurisubharmonic functions on the octonionic plane and Spin(9)-invariant valuations on convex sets
Metric Geometry
2016-07-27 v4 Complex Variables
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.
Keywords
Cite
@article{arxiv.0707.4385,
title = {Plurisubharmonic functions on the octonionic plane and Spin(9)-invariant valuations on convex sets},
author = {Semyon Alesker},
journal= {arXiv preprint arXiv:0707.4385},
year = {2016}
}
Comments
35 pages. The definition of octonionic Hessian is replaced with the transposed matrix as it should be. Other minor corrections