Geodesic
Delta-extremal functions in $\mathbb{C}^n$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 3, pp. 389-398

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The article is devoted to properties of a weighted Green function. We study the $(\delta,\psi)$-extremal Green function $V^{*}_{\delta}(z,K,\psi)$ defined by the class $\mathcal{L}_{\delta}=\big\{u(z)\in psh(\mathbb C^{n}):\ u(z) \leqslant C_{u}+\delta\ln^{+}|z|, \ z\in\mathbb C^{n}\big\}, \ \delta>0.$ We see that the notion of regularity of points with respect to different numbers $\delta$ differ from each other. Nevertheless, we prove that if a compact set $K\subset\mathbb{C}^{n}$ is regular, then $\delta$-extremal function is continuous in the whole space $\mathbb C^{n}.$
Keywords: plurisubharmonic function, Green function, weighted Green function, $\delta$-extremal function. 
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     title = {Delta-extremal functions in $\mathbb{C}^n$},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2021_14_3_a11/}
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Nurbek Kh. Narzillaev. Delta-extremal functions in $\mathbb{C}^n$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 3, pp. 389-398. http://geodesic.mathdoc.fr/item/JSFU_2021_14_3_a11/