Weak continuity of the complex k-hessian operators with respect to local uniform convergence

Neil S. Trudinger; Wei Zhang

doi:10.1017/S0004972713000336

Weak continuity of the complex k-hessian operators with respect to local uniform convergence

Neil S. Trudinger^*, Wei Zhang

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

In this paper, we study the properties of k-plurisubharmonic functions defined on domains in ℂⁿ. By the monotonicity formula, we give an alternative proof of the weak continuity of complex k-Hessian operators with respect to local uniform convergence.

Original language	English
Pages (from-to)	227-233
Number of pages	7
Journal	Bulletin of the Australian Mathematical Society
Volume	89
Issue number	2
DOIs	https://doi.org/10.1017/S0004972713000336
Publication status	Published - Apr 2014

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title = "Weak continuity of the complex k-hessian operators with respect to local uniform convergence",

abstract = "In this paper, we study the properties of k-plurisubharmonic functions defined on domains in ℂn. By the monotonicity formula, we give an alternative proof of the weak continuity of complex k-Hessian operators with respect to local uniform convergence.",

keywords = "Complex Monge-Amp{\`e}re operator, complex k-Hessian measures, monotonicity formula, weak convergence",

author = "Trudinger, {Neil S.} and Wei Zhang",

year = "2014",

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AU - Zhang, Wei

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AB - In this paper, we study the properties of k-plurisubharmonic functions defined on domains in ℂn. By the monotonicity formula, we give an alternative proof of the weak continuity of complex k-Hessian operators with respect to local uniform convergence.

KW - Complex Monge-Ampère operator

KW - complex k-Hessian measures

KW - monotonicity formula

KW - weak convergence

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DO - 10.1017/S0004972713000336

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JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 2

ER -

Weak continuity of the complex k-hessian operators with respect to local uniform convergence

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