Abstract
We prove that in general it is not possible to extend a Lipschitz multiple valued function without increasing the Lipschitz constant, i.e. we show that there is no analog of Kirszbraun’s extension theorem for Almgren’s multiple valued functions.
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References
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Logaritsch, P., Marchese, A. Kirszbraun’s extension theorem fails for Almgren’s multiple valued functions. Arch. Math. 102, 455–458 (2014). https://doi.org/10.1007/s00013-014-0642-4
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DOI: https://doi.org/10.1007/s00013-014-0642-4