Stratification for the singular set of approximate harmonic maps

Aaron Naber, Daniele Valtorta*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The aim of this note is to extend the results in Naber and Valtorta (Ann Math (2) 185:131–227,, 2017) to the case of approximate harmonic maps. More precisely, we will proved that the singular strata Sk(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 Naber and Valtorta (2017), and in particular we produce a new main covering lemmas which vastly simplifies the older argument.

Original languageEnglish (US)
Pages (from-to)1415-1455
Number of pages41
JournalMathematische Zeitschrift
Issue number3-4
StatePublished - Dec 1 2018


  • Approximate harmonic maps
  • Quantitative stratification
  • Reifenberg theorem

ASJC Scopus subject areas

  • Mathematics(all)


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