### Extending hypersurfaces and meromorphic functions.

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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 $\left(L{B}^{\infty}\right)$ for the dual space of the space of germs of holomorphic functions on that compact set.

The aim of the present paper is to study meromorphic extension spaces. The obtained results allow us to get the invariance of meromorphic extendibility under finite proper surjective holomorphic maps.

It is shown that if E is a Frechet space with the strong dual E* then H(E*), the space of holomorphic functions on E* which are bounded on every bounded set in E*, has the property (DN) when E ∈ (DN) and that H(E*) ∈ (Ω) when E ∈ (Ω) and either E* has an absolute basis or E is a Hilbert-Frechet-Montel space. Moreover the complementness of ideals J(V) consisting of holomorphic functions on E* which are equal to 0 on V in H(E*) for every nuclear Frechet space E with E ∈ (DN) ∩ (Ω) is stablished when...

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

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 ${\Delta}_{*}$ into D can be extended holomorphically to a map from Δ into D.

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.

We prove a comparison principle for the log canonical threshold of plurisubharmonic functions under an assumption on complex Monge-Ampère measures.

We give some characterizations of the class ${}_{m}\left(\Omega \right)$ and use them to establish a lower estimate for the log canonical threshold of plurisubharmonic functions in this class.

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