Stratification for the singular set of approximate harmonic maps

Abstract

The aim of this note is to extend the results in arXiv:1504.02043 to the case of approximate harmonic maps. More precisely, we will proved that the singular strata $S^k(u)$ of an approximate harmonic map are k-rectifiable, and we will show effect bounds on the quantitative strata. In the process we will simplify many of the arguments from arXiv:1504.02043, and in particular we produce a new main covering lemmas which vastly simplifies the older argument.

References in corpus (1)

• Rectifiable-Reifenberg and the Regularity of Stationary and Minimizing Harmonic Maps

Cited by in corpus (3)

• Regularity of the free boundary for the vectorial Bernoulli problem
• Boundary unique continuation on $C^1$-Dini domains and the size of the singular set
• Stratification and rectifiability of harmonic map flows via tangent measures