On filling minimality of simple Finsler manifolds

TL;DR

This paper presents a formula relating the Holmes-Thompson volumes of simple Finsler manifolds to boundary distances and derivatives, leading to a new minimality condition for filling problems.

Contribution

It introduces a volume difference formula for simple Finsler manifolds and applies it to establish a preconditioned filling minimality result.

Findings

Derived a volume difference formula involving boundary distances

Established a preconditioned filling minimality criterion

Applicable to manifolds of arbitrary dimension

Abstract

This paper states a formula for the difference of the Holmes-Thompson volumes of two simple Finsler manifolds of arbitrary dimension, in terms of the boundary distances and their derivatives. An application is a preconditioned filling minimality result.