A remark on a generalized Suita conjecture for finite points case

TL;DR

This paper investigates a weighted version of the Suita conjecture for higher derivatives and finite points, using harmonic functions to establish conditions for equality when the harmonic component of the weight is trivial.

Contribution

It introduces new conditions for the equality case in a generalized Suita conjecture involving harmonic functions and finite points.

Findings

Identifies necessary and sufficient conditions for equality in the weighted Suita conjecture

Uses harmonic functions to analyze higher derivatives in the conjecture

Provides insights into the case when the harmonic part of the weight is trivial

Abstract

In this article, we use a class of harmonic functions (maybe multi-valued) to study the equality part in a weighted version of Suita conjecture for higher derivatives and finite points case, and we obtain some sufficient and necessary conditions for the equality part to hold when the harmonic part $u$ of the weight is trivial.