Propriété de stabilité de la fonction extrémale relative

Cross Theorems with Singularities

“…An example in [1] shows that, in general, ω(·, A, D) = ω(·, A, D) on D. Now we compare the plurisubharmonic measure ω(·, A, D) with Siciak's relative extremal function ω(·, A, D). For the moment, we only focus on the case where A ⊂ D.…”

A Generalization of the Annulus Formula for the Relative Extremal Function

“…Proof. The proof is the same as the one of Proposition 3.2.23 in [12]; only, we use Lemma 2.2 from [1] instead of Corollary 3.2.12.…”

“…The proof is the same as the proof of Proposition 3.2.15 from [12]. We only need to use Lemma 2.6 and Theorem 2.1 from [1] [13], Proposition 4.5.2). Let Y be an irreducible Stein space.…”

Recent developments in the theory of separately holomorphic mappings

“…An example in [3] shows that, in general, ω(·, A, D) = ω(·, A, D) on D. Section 6 and 9 below are devoted to the study of ω(·, A, D) in some important cases. As we will see later, in most applications one can obtain good and simple characterizations of ω(·, A, D) (see Theorem 5, 6, 7, 9 and Corollary 2, 3 below).…”

“…O(G, C)) separates points in D (resp. in G) 3 . Let M ⊂ W be a relatively closed subset which is pluripolar (resp.…”