On an upper bound of the Gaussian curvature for one class of nonregular surfaces (Q1901945)

The author investigates some properties of the Gaussian curvature of surfaces with cusps of negative curvature. The main result is the following theorem: Let \(F\) be a complete bounded surface of the space \(E_3\), whose regular part belongs to the class \(C^2\). If the Gaussian curvature \(K\) of the surface \(F\) is negative and the boundary of \(F\) consists of a finite number of vertices of cusps, and each cusp is one of the surfaces \(F_0\), \(F_{00}\), \(F_1\) or \(F_2\) in a small neighborhood of its vertex, then \(\sup K=0\).