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<p>In this paper we consider sphere-valued stationary/minimizing fractional harmonic mappings introduced in recent years by several authors, especially by Millot et al. (Arch Ration Mech Anal 242:747–825, 2021) and Millot and Sire (Arch Ration Mech Anal 215:125–210, 2015). 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 and Naber (Commun Pure Appl Math 66(6):965–990, 2013), from which a global regularity estimates follows.</p>

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A global regularity theory for sphere-valued fractional harmonic maps

  • 期刊论文

  • 发表日期：

    2025年10月16日

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  • Yu He,
  • Chang-Lin Xiang,
  • Gao-Feng Zheng

摘要

In this paper we consider sphere-valued stationary/minimizing fractional harmonic mappings introduced in recent years by several authors, especially by Millot et al. (Arch Ration Mech Anal 242:747–825, 2021) and Millot and Sire (Arch Ration Mech Anal 215:125–210, 2015). 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 and Naber (Commun Pure Appl Math 66(6):965–990, 2013), from which a global regularity estimates follows.