Stratification for the singular set of approximate harmonic maps

TL;DR

This paper extends previous results on harmonic maps to approximate harmonic maps, demonstrating rectifiability of singular strata and providing bounds, with simplified proofs and new covering lemmas.

Contribution

It generalizes the rectifiability and stratification results to approximate harmonic maps and introduces simplified arguments and new covering lemmas.

Findings

Singular strata of approximate harmonic maps are k-rectifiable.

Quantitative bounds on the strata are established.

Simplified proofs and new covering lemmas are provided.

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.