Quaternionic Monge-Ampère equations

Semyon Alesker

doi:10.1007/BF02930695

Quaternionic Monge-Ampère equations

Semyon Alesker^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

The main result of this article is the existence and uniqueness of the solution of the Dirichlet problem for quaternionic Monge-Ampère equations in quaternionic strictly pseudoconvex bounded domains in ℍ ⁿ . We continue the study of the theory of plurisubharmonic functions of quaternionic variables started by the author at [2].

Original language	English
Pages (from-to)	205-238
Number of pages	34
Journal	Journal of Geometric Analysis
Volume	13
Issue number	2
DOIs	https://doi.org/10.1007/BF02930695
State	Published - 2003

Keywords

Monge-Ampére
equations
non-commutative determinants
plurisubharmonic functions
quaternions

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10.1007/BF02930695

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abstract = "The main result of this article is the existence and uniqueness of the solution of the Dirichlet problem for quaternionic Monge-Amp{\`e}re equations in quaternionic strictly pseudoconvex bounded domains in ℍ n . We continue the study of the theory of plurisubharmonic functions of quaternionic variables started by the author at [2].",

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AB - The main result of this article is the existence and uniqueness of the solution of the Dirichlet problem for quaternionic Monge-Ampère equations in quaternionic strictly pseudoconvex bounded domains in ℍ n . We continue the study of the theory of plurisubharmonic functions of quaternionic variables started by the author at [2].

KW - Monge-Ampére

KW - equations

KW - non-commutative determinants

KW - plurisubharmonic functions

KW - quaternions

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JO - Journal of Geometric Analysis

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Quaternionic Monge-Ampère equations

Abstract

Keywords

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