Minimal capacity points and the Lowest eigenfunctions

TL;DR

This paper explores the relationship between the point of minimal capacity in a domain and the lowest eigenfunction of the Laplacian, revealing a specific connection in certain cases.

Contribution

It introduces the concept of minimal capacity points and links them to the lowest eigenfunctions of the Laplacian in a particular setting.

Findings

Identifies the point of minimal capacity in a domain

Establishes a connection between minimal capacity points and lowest eigenfunctions

Provides insights into spectral properties related to domain geometry

Abstract

We introduce the concept of the point of minimal capacity of the domain, and observe a connection between this point and the lowest eigenfunction of a Laplacian on this domain, in one special case.