Removable singularities of plurisubharmonic functions of restricted growth
Matematičeskie zametki, Tome 64 (1998) no. 1, pp. 64-72
Cet article a éte moissonné depuis la source Math-Net.Ru
Let $G$ be a domain in $\mathbb C^n$, $n\ge2$, let $A$ be a connected complex $(n-1)$-dimensional submanifold of $G$, and let $\varphi$ be a plurisubharmonic function in $G\setminus A$. We obtain conditions on the growth of $\varphi$ that guarantee the local boundedness of $\varphi$ at a point a $a\in A\subset G$ and the existence of a plurisubharmonic extension of $\varphi$ to $G$.
@article{MZM_1998_64_1_a7,
author = {N. G. Karpova},
title = {Removable singularities of plurisubharmonic functions of restricted growth},
journal = {Matemati\v{c}eskie zametki},
pages = {64--72},
year = {1998},
volume = {64},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_1_a7/}
}
N. G. Karpova. Removable singularities of plurisubharmonic functions of restricted growth. Matematičeskie zametki, Tome 64 (1998) no. 1, pp. 64-72. http://geodesic.mathdoc.fr/item/MZM_1998_64_1_a7/
[1] Karpova N. G., “Ob ustranenii osobennostei plyurisubgarmonicheskikh funktsii”, Matem. zametki, 49:3 (1991), 35–40 | MR
[2] Siu Y.-T., “Analyticity of sets associated to Lelong numbers and the extension of closed positive currents”, Invent. Math., 27:1–2 (1974), 53–156 | DOI | MR | Zbl
[3] Chirka E. M., “Regulyarnost granits analiticheskikh mnozhestv”, Matem. sb., 117:3 (1982), 291–336 | MR | Zbl
[4] Chirka E. M., Kompleksnye analiticheskie mnozhestva, Nauka, M., 1985