Geodesic
On Analytic Multifunctions
Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 715-721

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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 $S_a=S\cap\{z=a\}$.
Keywords: analytic multifunction, subharmonic function, pseudoconcavity, pseudoconvexity, plurisubharmonicity, pluripolarity, capacity of a set, Hartogs series. 
@article{MZM_2008_83_5_a7,
     author = {A. S. Sadullaev},
     title = {On {Analytic} {Multifunctions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {715--721},
     publisher = {mathdoc},
     volume = {83},
     number = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a7/}
}
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A. S. Sadullaev. On Analytic Multifunctions. Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 715-721. http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a7/