The aim of this note is to extend the results in Naber and Valtorta (Ann Math (2) 185:131–227, https://doi.org/10.4007/annals.2017.185.1.3, 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.
Naber, A., Valtorta, D. (2018). Stratification for the singular set of approximate harmonic maps. MATHEMATISCHE ZEITSCHRIFT, 290(3-4), 1415-1455 [10.1007/s00209-018-2068-3].
Stratification for the singular set of approximate harmonic maps
Valtorta, D
2018
Abstract
The aim of this note is to extend the results in Naber and Valtorta (Ann Math (2) 185:131–227, https://doi.org/10.4007/annals.2017.185.1.3, 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.
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