A remark on a weighted version of Suita conjecture for higher derivatives

TL;DR

This paper investigates a weighted version of the Suita conjecture for higher derivatives, exploring the conditions for equality and their relation to harmonic functions and Dirichlet problems in planar domains.

Contribution

It introduces a weighted Suita conjecture for higher derivatives and establishes new relations between equality sets, harmonic functions, and Dirichlet problems in bounded planar domains.

Findings

Characterization of equality points in the weighted Suita conjecture

Relations between harmonic functions and the equality set

Connections to Dirichlet problem solutions

Abstract

In this article, we consider the set of points for the holding of the equality in a weighted version of Suita conjecture for higher derivatives, and give relations between the set and the integer valued points of a class of harmonic functions (maybe multi-valued). For planar domains bounded by finite analytic closed curves, we give relations between the set and Dirichlet problem.