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

Published online by Cambridge University Press:  11 June 2013

NEIL S. TRUDINGER*
Affiliation:
Centre for Mathematics and its Applications, The Australian National University, Canberra, ACT 0200, Australia email [email protected]
WEI ZHANG
Affiliation:
Centre for Mathematics and its Applications, The Australian National University, Canberra, ACT 0200, Australia email [email protected]
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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.

Type
Research Article
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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