# Harmonic Coordinates for the Nonlinear Finsler Laplacian and Some Regularity Results for Berwald Metrics

## TL;DR

This paper establishes the existence of harmonic coordinates for the nonlinear Finsler Laplacian and explores their applications, including a Finsler version of the Myers–Steenrod theorem, with partial regularity results for Berwald metrics.

## Contribution

It introduces harmonic coordinates for the nonlinear Finsler Laplacian and applies them to prove a Finsler analogue of the Myers–Steenrod theorem, with new partial regularity results for Berwald metrics.

## Key findings

- Existence of harmonic coordinates for the nonlinear Finsler Laplacian.
- Application to a Finsler version of the Myers–Steenrod theorem.
- Partial regularity results for Berwald metrics.

## Abstract

We prove existence of harmonic coordinates for the nonlinear Laplacian of a Finsler manifold and apply them in a proof of the Myers--Steenrod theorem for Finsler manifolds. Different from the Riemannian case, these coordinates are not suitable for studying optimal regularity of the fundamental tensor, nevertheless, we obtain some partial results in this direction when the Finsler metric is Berwald.