Special polyhedra for Reinhardt domains

TL;DR

This paper demonstrates that all bounded hyperconvex Reinhardt domains can be approximated by specific polynomial polyhedra using homogeneous polynomial mappings, via approximation of their pluricomplex Green functions.

Contribution

It introduces a method to approximate hyperconvex Reinhardt domains with special polynomial polyhedra through Green function approximation.

Findings

Bounded hyperconvex Reinhardt domains can be approximated by polynomial polyhedra.

Approximation uses homogeneous polynomial mappings.

Green function approximation is key to the method.

Abstract

We show that every bounded hyperconvex Reinhardt domain can be approximated by special polynomial polyhedra defined by homogeneous polynomial mappings. This is achieved by means of approximation of the pluricomplex Green function of the domain with pole at the origin.