Regularity of weakly harmonic maps from a Finsler surface into an n-sphere

Xiaohuan Mo and Liang Zhao

Vol. 253 (2011), No. 1, 145–155

DOI: 10.2140/pjm.2011.253.145

Abstract

We study harmonic maps on Finsler surfaces. Using Berwald frames on Finsler surfaces, we prove conformal invariance for the energy of Finsler harmonic maps. As an application, we show that weakly harmonic maps from a Finsler surface to a sphere 𝕊ⁿ are in fact smooth by establishing a new Jacobi structure, generalizing the regularity result previously known for the case of a harmonic map from a Riemannian surface.

Keywords

Finsler surface, conformal invariance, weakly harmonic map, regularity

Mathematical Subject Classification 2000

Primary: 53C60

Secondary: 54E40

Milestones

Received: 13 August 2010

Revised: 19 June 2011

Accepted: 22 August 2011

Published: 28 November 2011