On 2-dimensional surfaces in 3-dimensional and 4-dimensional Euclidean spaces. Results and unsolved problems

  • Yu. A. Aminov


We present a survey of the results obtained for 2-dimensional surfaces in $E^3$ and $E^4$ and connected with the Gaussian curvature and Gaussian torsion. In this connection, we consider the Monge –Amp´ere equations, obtain the generalizations of Bernstein’s integral formula, and establish some lower estimates for the exterior diameter of surfaces in $E^3$.
How to Cite
Aminov, Y. A. “On 2-Dimensional Surfaces in 3-Dimensional and 4-Dimensional Euclidean spaces. Results and Unsolved Problems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 1, Jan. 2019, pp. 3-36, https://umj.imath.kiev.ua/index.php/umj/article/view/1416.
Research articles