In this article we extend to arbitrary p-energy minimizing maps between Riemannian manifolds a regularity result which is known to hold in the case \(p=2\). We first show that the set of singular points of such a map can be quantitatively stratified: we classify singular points based on the number of almost-symmetries of the map around them, as done in Cheeger and Naber (Commun Pure Appl Math 66(6): 965–990, 2013). Then, adapting the work of Naber and Valtorta (Ann Math (2) 185(1): 131–227, 2017), we apply a Reifenberg-type Theorem to each quantitative stratum; through this, we achieve an upper bound on the Minkowski content of the singular set, and we prove it is k-rectifiable for a k which only depends on p and the dimension of the domain.

在本文中，我们将黎曼流形之间的任意p-能量最小化映射扩展为已知的规则性结果，该情况在\（p = 2 \）情况下成立。我们首先展示了这种地图的奇异点集可以进行定量分层：我们根据围绕其的地图的几乎对称数对奇异点进行分类，就像在Cheeger和Naber中所做的那样（Commun Pure Appl Math 66（6 ）：965–990，2013年）。然后，改编Naber和Valtorta的工作（Ann Math（2）185（1）：131–227，2017年），我们对每个量化层次应用Reifenberg型定理；通过这一点，我们实现了对单数集的闵可夫斯基内容的上限，并证明它是ķ -rectifiable用于ķ它仅取决于p和域的维数。