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<p>In this paper, we study the geometric properties of the singular sets of the stationary approximate biharmonic maps. Such singular sets can be stratified similar as the one introduced by Cheeger and Naber (Commun Pure Appl Math 66:965–990, 2013) for harmonic maps. Adapting the Naber–Valtorta theory (Ann Math 2(185):131–227, 2017), we derive the Minkowski content estimates and rectifiability of the quantitative strata of the singular sets. As a result, we obtain a regularity result for these maps under some geometric assumptions on the target Riemannian manifold <i>N</i>.</p>

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Quantitative Stratification for Singular Set of Stationary Approximate Biharmonic Maps

  • 期刊论文

  • 发表日期：

    2025年2月6日

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  • Gui-Chun Jiang,
  • Gao-Feng Zheng

摘要

In this paper, we study the geometric properties of the singular sets of the stationary approximate biharmonic maps. Such singular sets can be stratified similar as the one introduced by Cheeger and Naber (Commun Pure Appl Math 66:965–990, 2013) for harmonic maps. Adapting the Naber–Valtorta theory (Ann Math 2(185):131–227, 2017), we derive the Minkowski content estimates and rectifiability of the quantitative strata of the singular sets. As a result, we obtain a regularity result for these maps under some geometric assumptions on the target Riemannian manifold N.