The equivalence of isocapacitary notions of mass

TL;DR

This paper proves that different isocapacitary definitions of mass in geometric analysis are equivalent, unifying various approaches including Huisken's isoperimetric mass and Jauregui's isocapacitary mass.

Contribution

It establishes the equivalence of multiple isocapacitary notions of mass, clarifying their relationship in geometric measure theory.

Findings

Proves the equivalence of isocapacitary mass notions

Includes Huisken's isoperimetric mass as a special case

Unifies different definitions of mass in geometric analysis

Abstract

In this short note, we will prove the equivalence of the isocapacitary notions of mass. This family also includes G. Huisken's isoperimetric mass and J. L. Jauregui's isocapacitary mass.