Local geodesics between toric plurisubharmonic functions with infinite energy

TL;DR

This paper investigates the behavior of weak geodesics between toric plurisubharmonic functions with infinite energy, providing a characterization of convergence conditions using Lelong numbers in complex analysis.

Contribution

It offers a new characterization of convergence along geodesics between toric psh functions with poles, expanding understanding of their geometric behavior.

Findings

Convergence condition characterized by Lelong numbers.

Analysis focused on functions with poles at the origin.

Results applicable to pseudoconvex domains in complex analysis.

Abstract

Our interest is the behavior of weak geodesics between two plurisubharmonic functions on pseudoconvex domains. We characterize the convergence condition along the geodesic between toric psh functions with a pole at origin on a unit ball in $\mathbb{C}^n$ by means of Lelong numbers.