Minimizing fractional harmonic maps on the real line in the supercritical regime

TL;DR

This paper investigates the regularity of fractional harmonic maps from an interval into manifolds, proving H"older continuity away from finite sets and everywhere for the sphere, in the supercritical regime where s<1/2.

Contribution

It establishes new regularity results for minimizing fractional harmonic maps in the supercritical regime, including full regularity for maps into the sphere.

Findings

H"older continuity away from a finite set for general targets

Full H"older continuity for maps into the sphere

Addresses regularity in the supercritical fractional regime

Abstract

This article addresses the regularity issue for minimizing fractional harmonic maps of order $s\in(0,1/2)$ from an interval into a smooth manifold. H\"older continuity away from a locally finite set is established for a general target. If the target is the standard sphere, then H\"older continuity holds everywhere.