Pluripotential theory on quaternionic manifolds

Details Pluripotential theory on quaternionic manifolds Pluripotential theory on quaternionic manifolds

2010-10-18

arxiv.org/abs/1010.3534v4

Mathematics

Complex Variables

30 pages. Revised version

Scientific paper

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.

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