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

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.