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The polynomial sub-Riemannian differentiability of some Hölder map**s of Carnot groups

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Abstract

The polynomial sub-Riemannian differentiability is established for the large classes of Hölder map**s in the sub-Riemannian sense, namely, the classes of smooth map**s, their graphs, and the graphs of Lipschitz map**s in the sub-Riemannian sense defined on nilpotent graded groups. We also describe some special bases that carry the sub-Riemannian structure of the preimage to the image.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    M. B. Karmanova

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  1. M. B. Karmanova
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Correspondence to M. B. Karmanova.

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The author was supported by the Russian Foundation for Basic Research (Grant 16–31–60036–mol–a–dk).

Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 2, pp. 305–332, March–April, 2017; DOI: 10.17377/smzh.2017.58.206.

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Karmanova, M.B. The polynomial sub-Riemannian differentiability of some Hölder map**s of Carnot groups. Sib Math J 58, 232–254 (2017). https://doi.org/10.1134/S0037446617020069

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  • DOI: https://doi.org/10.1134/S0037446617020069

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