Regularity theory on fractional harmonic mappings

In this talk, we consider sphere-valued stationary/minimizing fractional harmonic mappings introduced in recent years by several authors, especially by MillotPegon-Schikorra and Millot-Sire. Based on their rich partial regularity theory, we establish a quantitative stratification theory for singular sets of these mappings by making use of the quantitative differentiation approach of Cheeger-Naber, from which a global regularity estimates follows.

This is joint work with Yu He and Chang-Lin Xiang.