Potential theory for quaternionic plurisubharmonic functions
نویسندگان
چکیده
منابع مشابه
Quaternionic linear algebra and plurisubharmonic functions of quaternionic variables
Quaternionic linear algebra and plurisubharmonic functions of quaternionic variables. Abstract We remind known and establish new properties of the Dieudonné and Moore determinants of quaternionic matrices. Using these linear algebraic results we develop a basic theory of plurisubharmonic functions of quaternionic variables. The main point of this paper is that in quaternionic algebra and analys...
متن کاملNon-commutative linear algebra and plurisubharmonic functions of quaternionic variables
We remind known and establish new properties of the Dieudonné and Moore determinants of quaternionic matrices. Using these linear algebraic results we develop a basic theory of plurisubharmonic functions of quaternionic variables.
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The paper is a survey of the recent theory of plurisubharmonic functions of quaternionic variables, together with its applications to the theory of valuations on convex sets and HKT-geometry (Hyper-Kähler with Torsion). The exposition follows some earlier papers by the author and a joint paper by Verbitsky and the author.
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The main objective of this paper is to prove a new inequality for plurisubharmonic functions estimating their supremum over a ball by their supremum over a measurable subset of the ball. We apply this result to study local properties of polynomial, algebraic and analytic functions. The paper has much in common with an earlier paper [Br] of the author.
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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 [4], [5], [7] by the author and [8] by M. Verbitsky and the author.
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2017
ISSN: 0026-2285
DOI: 10.1307/mmj/1488510022