Reflection Principle for the Complex Monge-Ampere Equation and Plurisubharmonic Functions

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Koskenoja , M 2019 , ' Reflection Principle for the Complex Monge-Ampere Equation and Plurisubharmonic Functions ' , Advances in Applied Clifford Algebras , vol. 29 , no. 4 , 68 . https://doi.org/10.1007/s00006-019-0984-x

Title: Reflection Principle for the Complex Monge-Ampere Equation and Plurisubharmonic Functions
Author: Koskenoja, Mika
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2019-09
Number of pages: 14
Belongs to series: Advances in Applied Clifford Algebras
ISSN: 0188-7009
URI: http://hdl.handle.net/10138/304615
Abstract: We study reflection principle for several central objects in pluripotential theory. First we show that the odd reflected function gives an extension for pluriharmonic functions over a flat boundary. Then we show that the even reflected function gives an extension for nonnegative plurisubharmonic functions. In particular cases odd and/or even reflected functions give extensions for classical solutions of the homogeneous complex Monge-Ampere equation. Finally, we state reflection principle for the generalized complex Monge-Ampere equation and maximal plurisubharmonic functions.
Subject: 111 Mathematics
Reflection principle
Complex Monge-Ampere equation
Homogeneous equation
Pluriharmonic
Plurisubharmonic
Pluripotential theory
Several complex variables
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