Geodesic
An estimate for polynomials on analytic sets
Izvestiya. Mathematics , Tome 20 (1983) no. 3, pp. 493-502.

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Let $A$ be a connected, analytic (in general, not closed) subset of the complex space $\mathbf C^n$ and let $K\subset A$ be a compact set which is not pluri-polar in $A$. In this article it is proved that the extremal function $V(z,K)$ is locally bounded on $A$ if and only if $A$ belongs to some algebraic set of the same dimension as $A$. Moreover, it is shown that for an algebraic set $A$ in a neighborhood of any ordinary point $z^0\in A_0$ the function $V(z,K)$ can be represented as the limit of an increasing sequence of maximal functions. Bibliography: 10 titles. 
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     title = {An estimate for polynomials on analytic sets},
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A. S. Sadullaev. An estimate for polynomials on analytic sets. Izvestiya. Mathematics , Tome 20 (1983) no. 3, pp. 493-502. http://geodesic.mathdoc.fr/item/IM2_1983_20_3_a4/

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