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Sharp Differentiability Results for the Lower Local Lipschitz Constant and Applications to Non-embedding

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Abstract

We give a sharp condition on the lower local Lipschitz constant of a mapping from a metric space supporting a Poincaré inequality to a Banach space with the Radon–Nikodym property that guarantees differentiability at almost every point. We apply these results to obtain a non-embedding theorem for a corresponding class of mappings.

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Acknowledgments

K. W. was supported by Academy of Finland Grant 128144, the Swiss National Science Foundation, European Research Council Project CG-DICE, and the European Science Council Project HCAA. T. Z. was supported by the Swiss National Science Foundation Grant PBBEP3_130157 and by the Academy of Finland Grant Number 251650.

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Correspondence to K. Wildrick.

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Communicated by Loukas Grafakos.

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Wildrick, K., Zürcher, T. Sharp Differentiability Results for the Lower Local Lipschitz Constant and Applications to Non-embedding. J Geom Anal 25, 2590–2616 (2015). https://doi.org/10.1007/s12220-014-9527-9

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  • DOI: https://doi.org/10.1007/s12220-014-9527-9

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