Quantitative stratification and global regularity for 1/2-harmonic mappings
Abstract
In this paper, we extend the celebrated global regularity theory of Naber-Valtorta [Ann. Math. 2017] to 1/2-harmonic mappings into manifolds. Inspired by their work, we first adapt Lin's defect measure theory [Ann. Math. 1999] to such maps building on the partial regularity established by Millot-Pegon-Schikorra [Arch. Ration. Mech. Anal. 2021]. Then apply it to show that the set of singular points of such maps can be quantitatively stratified via a new notion of boundary symmetry with the aid of {the celebrated harmonic extension method by Caffarelli-Silverstre}. As in that of Naber-Valtorta, developing the necessary quantitative regularity estimates, and then combining it with the Reifenberg type theorems and a delicate covering argument allow us to get sharp growth estimates on the volume of tubular neighborhood around singular points and establish the rectifiability of each singular stratum.
Cite
@article{arxiv.2603.12709,
title = {Quantitative stratification and global regularity for 1/2-harmonic mappings},
author = {Changyu Guo and Guichun Jiang and Changyou Wang and Changlin Xiang and Gaofeng Zheng},
journal= {arXiv preprint arXiv:2603.12709},
year = {2026}
}