$C^{1,\alpha}$-Regularity of energy minimizing maps from a 2-dimentional domain into a Finsler space

TL;DR

This paper proves that energy minimizing maps from 2D Riemannian domains into Finsler spaces are smooth to a certain degree, specifically $C^{1,eta}$ regularity, extending regularity results to Finsler geometries.

Contribution

The paper establishes $C^{1,eta}$ regularity for energy minimizing maps into Finsler spaces, a novel extension of regularity theory from Riemannian to Finsler geometry.

Findings

Energy minimizing maps are $C^{1,eta}$-regular.

Regularity results extend to Finsler spaces.

Provides foundational regularity theory for Finsler-valued harmonic maps.

Abstract

We show $C^{1,\alpha}$-regularity for energy minimizing maps from a 2-dimensional Riemannian manifold into a Finsler space $(\R^n, F)$ with a Finsler structure $F(u,X)$.