A minimum principle for plurisubharmonic functions

The main goal of this work is to give new and precise generalizations to various classes of plurisubharmonic functions of the classical minimum modulus principle for holomorphic functions of one complex variable, in the spirit of the famous lemma of Cartan-Boutroux. As an application we obtain precise estimates on the size of "plurisubharmonic lemniscates" in terms of appropriate Hausdorff contents

Open problems in pluripotential theory

We propose a list of open problems in pluripotential theory partially motivated by their applications to complex differential geometry. The list includes both local questions as well as issues related to the compact complex manifold setting.Comment: 27 page