Holomorphic minorants of (pluri-)subharmonic functions

TL;DR

This paper proves the existence of holomorphic minorants for plurisubharmonic functions, showing that a nonzero holomorphic function can be constructed with its logarithm bounded by local averages of the given function.

Contribution

It establishes a new existence result for holomorphic minorants of plurisubharmonic functions, advancing understanding in complex analysis and potential theory.

Findings

Existence of nonzero holomorphic functions bounded by local averages of plurisubharmonic functions

Extension of classical minorant results to the pluripotential setting

Potential applications in complex analysis and mathematical modeling

Abstract

Let $u$ be a plurisubharmonic function. We prove the existence of a nonzero holomorphic function such that the logarithm of its modulus is not more than local averages of this function $u$. This is the abstract for scientific conference "Algebra, Analysis and Related Problems of Mathematical Modeling" (Vladikavkaz, June 26-27, 2015) dedicated to the 60th anniversary of Professor, Doctor of Physical and Mathematical Sciences Vladimir A. Koibaev