Quantitative regularity for minimizing intrinsic fractional harmonic maps
Y. -Y. Wang, C. -L. Xiang, G. -F. Zheng
Published: 2025/9/29
Abstract
In this note, we study compactness and regularity theory of minimizing intrinsic fractional harmonic mappings introduced by Moser and Roberts. Based on the partial regularity theory of Moser and Roberts, we first use the modified Luckhaus lemma of Roberts to deduce compactness of these mappings, and then develop volume estimates of singular sets by the quantitative stratification theory of Cheeger and Naber. Combining these two results lead to a global regularity estimates which, in turn, allow us to obtain an improvement of the dimension estimate of singular sets.