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

3 Citations (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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doi = "10.1017/S0004972713000336",

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T1 - Weak continuity of the complex k-hessian operators with respect to local uniform convergence

AU - Trudinger, Neil S.

AU - Zhang, Wei

PY - 2014/4

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N2 - 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.

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

UR - https://www.scopus.com/pages/publications/84902130574

U2 - 10.1017/S0004972713000336

DO - 10.1017/S0004972713000336

M3 - Article

SN - 0004-9727

VL - 89

SP - 227

EP - 233

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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