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Stratification for the singular set of approximate harmonic maps

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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 \(\mathcal {S}^k(u)\) 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 Naber and Valtorta (2017), and in particular we produce a new main covering lemmas which vastly simplifies the older argument.

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Authors and Affiliations

  1. Northwestern University, Evanston, IL, USA

    Aaron Naber

  2. University of Zürich, Zürich, Switzerland

    Daniele Valtorta

Authors
  1. Aaron Naber
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  2. Daniele Valtorta
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Correspondence to Daniele Valtorta.

Additional information

Aaron Naber has been supported by National Science Foundation grant DMS-1406259, Daniele Valtorta has been supported by Swiss National Science Foundation project 200021_159403/1.

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Naber, A., Valtorta, D. Stratification for the singular set of approximate harmonic maps. Math. Z. 290, 1415–1455 (2018). https://doi.org/10.1007/s00209-018-2068-3

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  • DOI: https://doi.org/10.1007/s00209-018-2068-3

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