A note on the weighted log canonical thresholds of plurisubharmonic functions
type: Item
instance of: scholarly article
title: A note on the weighted log canonical thresholds of plurisubharmonic functions
zbMATH Open document ID: 1404.32063
author: Nguyen Xuan Hong
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2018-08-14T00:00:00Z
review text: The author gives a condition for the integrability of the expression \[ \int _{\Delta ^n} ||z||^{2t}e^{-2u} dV \] (where \(\Delta ^n\) is the unit polydisc, \(u\) a plurisubharmonic function locally bounded except for the origin, and \(dV\) denotes the Lebesgue measure) in terms of integrals over 1-dimensional (coordinate) slices. As a consequence he gets the following inequality for \(u\) having zero boundary values and the Monge-Ampère mass equal to the Dirac delta at the origin: \[ c_{t+1} (u)\geq c_t (u) +\frac{(n-1)^{n-1} }{c_t (u)^{n-1} } \] where \[ c_t (u)= \sup \big\{ c\geq 0: ||z||^{2t}e^{-2cu} \text{ is integrable near } 0 \big\}. \]
Mathematics Subject Classification ID: 32U05
Mathematics Subject Classification ID: 32U15
Mathematics Subject Classification ID: 32W20
zbMATH DE Number: 6917463
zbMATH Keywords: plurisubharmonic functions
zbMATH Keywords: log canonical thresholds
reviewed by: Slawomir Kołodziej
MaRDI profile type: Publication
full work available at URL: j.crma.2018.06.003
OpenAlex ID: W2809650389
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Wikidata QID: Q129622376
DOI: 10.1016/J.CRMA.2018.06.003
description: scientific article; zbMATH DE number 6917463