An improved lower bound for the logarithmic energy on $\mathbb S^2$

TL;DR

This paper improves the lower bound for the constant in the asymptotic expansion of minimal logarithmic energy on the sphere, advancing understanding of energy distribution on spherical surfaces.

Contribution

It provides a tighter lower bound for the logarithmic energy constant on 2, using established results to refine previous estimates.

Findings

Enhanced lower bound for the logarithmic energy constant on 2

Refined asymptotic analysis of minimal energy configurations

Improved understanding of energy distribution on spherical surfaces

Abstract

In this short note, we employ well-known results to improve the lower bound for the constant associated with the linear term in the asymptotic expansion of the minimal logarithmic energy on the sphere.