Monge-Amp\`ere measure at the boundary of some domains with corners

Abstract

Let $\mu^z$ be the measure obtained by sweeping out the Monge-Amp\`ere measure of the pluricomplex Green function with pole at $z. $ We prove that $\mu^z$ vanish on Levi flat parts of the boundary for 1) every relatively compact analytic polyhedron in complex space, 2) product domains of hyperconvex sets in Stein manifolds.