Some sufficient conditions for immersion in the large of metrics of positive curvature

It is proved that a regular Riemannian manifold diffeomorphic to a circle and having positive Gaussian curvature bounded from zero is immersible into a three-dimensional Euclidean space in the form of a regular surface if it has smallL_p (the norm of the gradient of Gaussian curvature), p > 2, or if it has a sufficiently small area (with any behavior of the geodesic boundary curvature).Translated from Ukrainskii Geometricheskii Sbornik, No. 34, pp. 51–59, 1991.