Capacity on Finsler Spaces

TL;DR

This paper introduces the concept of electric capacity in Finsler spaces, proving its conformal invariance, thereby advancing understanding of global Finsler geometry and its applications in mathematics and physics.

Contribution

It defines electric capacity on Finsler spaces and proves its fundamental conformal invariance property, a novel result in this geometric context.

Findings

Capacity of a compact set is conformal invariant on Finsler manifolds

The work bridges Finsler geometry with potential theory

Provides new tools for applications in physics and geometry

Abstract

Here, the concept of electric capacity on Finsler spaces is introduced and the fundamental conformal invariant property is proved, i.e. the capacity of a compact set on a connected non-compact Finsler manifold is conformal invariant. This work enables mathematicians and theoretical physicists to become more familiar with the global Finsler geometry and one of its new applications.