Armen Edigarian

Invariance of the pluricomplex green function under proper mappings with applications

In the paper we utilize the formula describing the behaviour of the pluricomplex Green function with many poles under proper holomorphic mappings to find the effective for-mulas for the function in the unit ball in with two poles.

Schwarz lemma for the tetrablock

We describe all complex geodesics in the tetrablock passing through the origin thus obtaining the form of all extremals in the Schwarz Lemma for the tetrablock. Some other extremals for the Lempert function and geodesics are also given. The paper may be seen as a continuation of the results from (2). The proofs rely on a necessary form of complex geodesics in general domains which is also proven in the paper.

Relative extremal functions and characterization of pluripolar sets in complex manifolds

We study a disc formula for the relative extremal function for a subset of a complex manifold and apply it to give a description of pluripolar sets and polynomial hulls.

Pluripolar hulis and holomorphic coverings

The aim of the paper is to study the behavior of (complete) pluripolar sets under special holomorphic mappings (proper mappings and coverings).