Homogeneous Plurisubharmonic Polynomials in Higher Dimensions

TL;DR

This paper investigates homogeneous plurisubharmonic polynomials in higher dimensions and their role in constructing local bumpings at boundary points of certain pseudoconvex domains, advancing understanding in several complex variables.

Contribution

It provides new results on homogeneous plurisubharmonic polynomials in multiple complex variables, relevant to boundary regularity in complex analysis.

Findings

Results on properties of homogeneous plurisubharmonic polynomials

Applications to local bumping constructions at boundary points

Insights into finite D'Angelo type pseudoconvex domains

Abstract

We prove several results on homogeneous plurisubharmonic polynomials on $\mathbb{C}^n$, $n\in\mathbb{Z}_{\geq 2}$. Said results are relevant to the problem of constructing local bumpings at boundary points of pseudoconvex domains of finite D'Angelo $1$-type in $\mathbb{C}^{n+1}$.