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An example of a C 1-smooth function whose gradient range is an arc with no tangent at any point

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Abstract

We construct an example of a C 1-smooth real function of two variables whose gradient range is an arc with no tangent at any point.

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References

  1. Korobkov M. V., “An analog of Sard’s theorem for C 1-smooth functions of two variables,” Siberian Math. J., 47, No. 5, 889–897 (2006).

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  3. Korobkov M. V. and Panov E. Yu., “Necessary and sufficient conditions for a curve to be the gradient range of a C 1-smooth function,” Siberian Math. J., 38, No. 4, 789–810 (2007).

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  4. Korobkov M. V., “Properties of the C 1-smooth functions with nowhere dense gradient range,” Siberian Math. J., 48, No. 6, 1019–1028 (2007).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    M. V. Korobkov

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  1. M. V. Korobkov
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Correspondence to M. V. Korobkov.

Additional information

Original Russian Text Copyright © 2008 Korobkov M. V.

The author was partially supported by the Russian Foundation for Basic Research (Grant 05-01-00482-a), the Russian Science Support Foundation for the Young Candidates of Sciences, and the Lavrent’ev Young Scientists Competition (No. 5).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 1, pp. 134–144, January–February, 2008.

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Korobkov, M.V. An example of a C 1-smooth function whose gradient range is an arc with no tangent at any point. Sib Math J 49, 109–116 (2008). https://doi.org/10.1007/s11202-008-0010-3

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  • DOI: https://doi.org/10.1007/s11202-008-0010-3

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