Pluripotential theory on quaternionic manifolds
Complex Variables
2011-12-09 v4
Abstract
On any quaternionic manifold of dimension greater than 4 a class of plurisubharmonic functions (or, rather, sections of an appropriate line bundle) is introduced. Then a Monge-Amp\`ere operator is defined. It is shown that it satisfies a version of theorems of A. D. Alexandrov and Chern-Levine-Nirenberg. These notions and results were previously known in the special case of hypercomplex manifolds. One of the new technical aspects of the present paper is the systematic use of the Baston differential operators, for which we prove a new multiplicativity property.
Cite
@article{arxiv.1010.3534,
title = {Pluripotential theory on quaternionic manifolds},
author = {Semyon Alesker},
journal= {arXiv preprint arXiv:1010.3534},
year = {2011}
}
Comments
30 pages. Revised version