Geodesic
Subextension of plurisubharmonic functions without changing the Monge–Ampère measures and applications
Le Mau Hai1 ; Nguyen Xuan Hong1
1 Department of Mathematics Hanoi National University of Education Hanoi, Vietnam
Annales Polonici Mathematici, Tome 112 (2014) no. 1, pp. 55-66 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The aim of the paper is to investigate subextensions with boundary values of certain plurisubharmonic functions without changing the Monge–Ampère measures. From the results obtained, we deduce that if a given sequence is convergent in $C_{n-1}$-capacity then the sequence of the Monge–Ampère measures of subextensions is weakly$^*$-convergent. As an application, we investigate the Dirichlet problem for a nonnegative measure $\mu $ in the class $\mathcal {F}(\varOmega ,g)$ without the assumption that $\mu $ vanishes on all pluripolar sets.
DOI : 10.4064/ap112-1-5
Keywords: the paper investigate subextensions boundary values certain plurisubharmonic functions without changing monge amp measures results obtained deduce given sequence convergent n capacity sequence monge amp measures subextensions weakly * convergent application investigate dirichlet problem nonnegative measure class mathcal varomega without assumption vanishes pluripolar sets

Le Mau Hai 1 ; Nguyen Xuan Hong 1

1 Department of Mathematics Hanoi National University of Education Hanoi, Vietnam 
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Le Mau Hai; Nguyen Xuan Hong. Subextension of plurisubharmonic functions without changing the Monge–Ampère measures and applications. Annales Polonici Mathematici, Tome 112 (2014) no. 1, pp. 55-66. doi: 10.4064/ap112-1-5

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