A global regularity theory for shpere-valued fractional harmonic maps
Abstract
In this paper we consider sphere-valued stationary/minimizing fractional harmonic mappings introduced in recent years by several authors, especially by Millot-Pegon-Schikorra Millot-Pegon-Schikorra-2021-ARMA and Millot-Sire Millot-Sire-15. 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 Cheeger-Naber-2013-CPAM, from which a global regularity estimates follows.
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