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Two-Dimensional Surfaces in 3-Dimensional and 4-Dimensional Euclidean Spaces. Results and Unsolved Problems

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Ukrainian Mathematical Journal Aims and scope

We present a survey of the results obtained for 2-dimensional surfaces in E3 and E4 and connected with the Gaussian curvature and Gaussian torsion. In this connection, we consider the Monge–Ampére equations, obtain the generalizations of Bernstein’s integral formula, and establish lower estimates for the outer diameter of the surfaces in E3.

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Authors and Affiliations

  1. Institute for Low Temperature Physics and Engineering, Ukrainian National Academy of Sciences, Kharkov, Ukraine

    Yu. A. Aminov

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Correspondence to Yu. A. Aminov.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 1, pp. 3–36, January, 2019.

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Aminov, Y.A. Two-Dimensional Surfaces in 3-Dimensional and 4-Dimensional Euclidean Spaces. Results and Unsolved Problems. Ukr Math J 71, 1–38 (2019). https://doi.org/10.1007/s11253-019-01622-x

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  • DOI: https://doi.org/10.1007/s11253-019-01622-x

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