Plurisubharmonic extremal functions and complex foliations for the complement of convex sets in \(\mathbf R^ n\) (Q1803911)

Some properties of J. Siciak's extremal function \(\Phi_ E\) are established in the case of compact subsets of \(\mathbb{R}^ n\). Moreover, a continuous complex foliation of the domain \(\mathbb{C}^ n\backslash E\) is effectively constructed by the leaves on which the plurisubharmonic extremal function \(u_ E\) is harmonic, in the case when an explicit representation of the extremal function is given.