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

  • E. A. Sevost'yanov


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.
How to Cite
Sevost’yanov, E. A. “On the Local Behavior of Sobolev Classes on Two-Dimensional Riemannian Manifolds”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 5, May 2019, pp. 663-76, https://umj.imath.kiev.ua/index.php/umj/article/view/1465.
Research articles