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Subextension of plurisubharmonic functions without changing the Monge-Ampère measures and applications

100%

Hai L. , Hong N.

Annales Polonici Mathematici

2014

tom 112

nr 1

55-66

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 μ in the class ℱ(Ω,g) without the assumption that μ vanishes on all pluripolar sets.

The non-pluripolarity of compact sets in complex spaces and the property $(LB^{∞})$ for the space of germs of holomorphic functions

100%

Hai L. , Long T.

Studia Mathematica

2002

tom 150

nr 1

1-12

The aim of this paper is to establish the equivalence between the non-pluripolarity of a compact set in a complex space and the property $(LB^{∞})$ for the dual space of the space of germs of holomorphic functions on that compact set.

Remarks on pluripolar hulls

80%

Hai L. , Dieu N. , Long T.

Annales Polonici Mathematici

2004

tom 84

nr 3

225-236

The aim of the paper is to establish some results on pluripolar hulls and to define pluripolar hulls of certain graphs.

Some properties of Reinhardt domains

80%

Hai L. , Dieu N. , Tuyen N.

Annales Polonici Mathematici

2003

tom 82

nr 3

203-217

We first establish the equivalence between hyperconvexity of a fat bounded Reinhardt domain and the existence of a Stein neighbourhood basis of its closure. Next, we give a necessary and sufficient condition on a bounded Reinhardt domain D so that every holomorphic mapping from the punctured disk $Δ_*$ into D can be extended holomorphically to a map from Δ into D.

ω-pluripolar sets and subextension of ω-plurisubharmonic functions on compact Kähler manifolds

80%

Hai L. , Khue N. , Hiep P.

Annales Polonici Mathematici

2007

tom 91

nr 1

25-41

We establish some results on ω-pluripolarity and complete ω-pluripolarity for sets in a compact Kähler manifold X with fundamental form ω. Moreover, we study subextension of ω-psh functions on a hyperconvex domain in X and prove a comparison principle for the class 𝓔(X,ω) recently introduced and investigated by Guedj-Zeriahi.