Boundary behavior of extremal plurisubharmonic functions
Let \(G\) be a bounded convex domain in \(\mathbb{C}^ N\). The author introduces a function \(D_ G: \{z\in \mathbb{C}^ N: | z|=1\}\to ]0,\infty]\) (a kind of directional Lelong number) which measures the rate of approximation of \(\partial G\) by the level sets of the pluricomplex Green function for \(G\). The function \(D_ G\) is shown to be connected with the boundary behavior of the Siciak extremal plurisubharmonic function for \(G\). The problem of the boundedness of the function \(D_ G\) is considered.
scientific article; zbMATH DE number 590324
scientific article