Regularity and quantification for harmonic maps with free boundary

TL;DR

This paper establishes a quantification result for harmonic maps with free boundary conditions from Riemannian surfaces into the unit ball, extending previous work from the disc case to more general surfaces.

Contribution

It generalizes existing quantification results for harmonic maps with free boundary from the disc to arbitrary Riemannian surfaces.

Findings

Proves a new quantification result for harmonic maps with free boundary.

Extends previous results from the disc to general Riemannian surfaces.

Provides bounds on the energy of harmonic maps with free boundary.

Abstract

We prove a quantification result for harmonic maps with free boundary from arbitrary Riemannian surfaces into the unit ball of ${\mathbb R}^{n+1}$ with bounded energy. This generalizes results obtained by Da Lio on the disc.