On the local behavior of Sobolev classes on two-dimensional Riemannian manifolds

Abstract

UDC 517.9
We study open discrete maps of two-dimensional Riemannian manifolds from the Sobolev class. For these mappings, we obtain the lower estimates of distortions of the moduli of the families of curves. As a consequence, we establish the equicontinuity of Sobolev classes at interior points of the domain.