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A note on Alberti’s Luzin-type theorem for gradients

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Abstract

We give a “soft” proof of Alberti’s Luzin-type theorem in Alberti (J Funct Anal 100:110–118, 1991), using elementary geometric measure theory and topology. Applications to the \(C^2\)-rectifiability problem are also discussed.

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Acknowledgements

SL is indebted to Ulrich Menne for kind communication and comments on the higher-order rectifiability problem. We also thank Yuchen Wang for her help on typesetting.

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  1. Department of Mathematics, Rice University, MS 136, P.O. Box 1892, Houston, TX, 77251, USA

    Siran Li

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  1. Siran Li
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Li, S. A note on Alberti’s Luzin-type theorem for gradients. Ricerche mat 70, 479–488 (2021). https://doi.org/10.1007/s11587-020-00485-w

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  • DOI: https://doi.org/10.1007/s11587-020-00485-w

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