A counterexample to the strong subadditivity of extremal plurisubharmonic functions
type: Item
instance of: scholarly article
title: A counterexample to the strong subadditivity of extremal plurisubharmonic functions
zbMATH Open document ID: 0637.32012
DOI: 10.1007/BF01636932
author: Johan Thorbiörnson
published in: Monatshefte für Mathematik
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178379
review text: A simple example is given which shows that one may have \[ h_ E(a)+ h_ F(a)> h_{E\cup F}(a)+ h_{E\cap F}(a) \] for some point \(a\in \Omega\), where \[ h_ E(z)=\sup \{u(z): u\in PSH(\Omega),\quad u\leq 0\quad on\quad E,\quad u\leq 1\quad in\quad \Omega \},\quad z\in \Omega, \] is the extremal function often studied.
Mathematics Subject Classification ID: 32U05
Mathematics Subject Classification ID: 31C10
Mathematics Subject Classification ID: 31C15
zbMATH DE Number: 4038213
zbMATH Keywords: extremal plurisubharmonic function
zbMATH Keywords: capacity
zbMATH Keywords: strong subadditivity
MaRDI profile type: Publication
Wikidata QID: Q124866573
cites work: A new capacity for plurisubharmonic functions
cites work: On the conjecture of the equivalence of the plurisubharmonic functions and the Hartogs functions
cites work: Capacities and extremal plurisubharmonic functions on subset of \(C^ n\).
cites work: Q5571891
cites work: Q3924489
cites work: Q3701749
description: scientific article; zbMATH DE number 4038213