On Analytic Multifunctions

A. S. Sadullaev

Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 715-721.

Résumé

For any multifunction $S\subset D_z\times\mathbb{C}_w$, we give a criterion for analyticity (pseudoconcavity) in terms of plurisubharmonicity of the function $V(z,w)=-\ln\rho(w,S_z)$, where $\rho(w,S_a)$ stands for the distance from the point $w$ to the set $S_a=S\cap\{z=a\}$.

Détail

Keywords: analytic multifunction, subharmonic function, pseudoconcavity, pseudoconvexity, plurisubharmonicity, pluripolarity, capacity of a set, Hartogs series.

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