# Intrinsic geometry and analysis of Finsler structures

## TL;DR

This paper proves that for certain Finsler structures on Euclidean domains, the intrinsic distance and differential structures are equivalent, clarifying their geometric relationship.

## Contribution

It establishes the equivalence of intrinsic distance and differential structures for weak upper semicontinuous admissible Finsler structures in Euclidean spaces.

## Key findings

- Intrinsic distance and differential structures coincide for the specified Finsler structures.
- The result applies to weak upper semicontinuous admissible Finsler structures.
- Clarifies the geometric relationship between different structures in Finsler geometry.

## Abstract

In this short note, we prove that if $F$ is a weak upper semicontinuous admissible Finsler structure on a domain in $\mathbb{R}^n$, $n\geq 2$, then the intrinsic distance and differential structures coincide.