arXiv math/06067562006-06math.MGmath.CV

Quaternionic plurisubharmonic functions and their applications to convexity

Semyon Alesker

备注：: 17 pages. The definition of quaternionic Hessian is replaced with a transposed matrix as it should be

英文摘要：

The goal of this article is to present a survey of the recent theory of plurisubharmonic functions of quaternionic variables, and its applications to theory of valuations on convex sets and HKT-geometry (HyperKähler with Torsion). The exposition follows the articles math.CV/0104209, math.CV/0208005, math.MG/0401219 by the author and math.CV/0510140 by M. Verbitsky and the author.

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