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WEAK CONTINUITY OF THE COMPLEX $k$-HESSIAN OPERATORS WITH RESPECT TO LOCAL UNIFORM CONVERGENCE

Part of: Differential operators in several variables Pluripotential theory Classical measure theory Other generalizations

Published online by Cambridge University Press:  11 June 2013

NEIL S. TRUDINGER  and
WEI ZHANG
NEIL S. TRUDINGER*
Affiliation:
Centre for Mathematics and its Applications, The Australian National University, Canberra, ACT 0200, Australia email wei.zhang@anu.edu.au
WEI ZHANG
Affiliation:
Centre for Mathematics and its Applications, The Australian National University, Canberra, ACT 0200, Australia email wei.zhang@anu.edu.au
*
✉neil.trudinger@anu.edu.au
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Abstract

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In this paper, we study the properties of $k$-plurisubharmonic functions defined on domains in ${ \mathbb{C} }^{n} $. 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–Ampère operatorcomplex k-Hessian measuresweak convergencemonotonicity formula

MSC classification

Secondary: 32W20: Complex Monge-Ampère operators 28A33: Spaces of measures, convergence of measures 32U05: Plurisubharmonic functions and generalizations 31C10: Pluriharmonic and plurisubharmonic functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 2 , April 2014 , pp. 227 - 233
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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