Variations of pseudoconvex domains in the complex manifold (Q1821913)

In an earlier paper [Proc. Japan Acad., Ser. A59, 289-292 (1983; Zbl 0578.32028)] the author had studied the notion of Robin's constant for pseudoconvex domains in \({\mathbb{C}}^ n\), and showed that if the domains vary holomorphically in a suitable sense, the Robin constant is a superharmonic function of the parameter. In this note, the author generalises the above result to the case of pseudoconvex domains in an arbitrary Kähler manifold, and gives an application to the problem of recognising Stein open subsets of complex homogeneous manifolds.