D. P. Ilyutko, E. A. Sevost'yanov, “On the local and boundary behaviour of inverse maps on Riemannian manifolds”, Mat. Sb., 2022, Volume 213, Number 1,Pages <nobr>46

This article is cited in 1 paper

On the local and boundary behaviour of inverse maps on Riemannian manifolds

D. P. Ilyutko^a, E. A. Sevost'yanov^bc

^a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
^b Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine
^c Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Slavyansk, Ukraine

Abstract: Results on the local behaviour of maps between Riemannian manifolds such that their inverses satisfy upper bounds on the distortion of the moduli of families of curves are obtained. For families of such maps theorems on their equicontinuity at interior points and boundary points of the domain are established.
Bibliography: 30 titles.

Keywords: Riemannian manifold, modulus of a family of curves, map with bounded distortion, map with finite distortion, inverse map, local behaviour of maps.

UDC: 517.548.2+514.764.2

MSC: 30C65, 58C07

Received: 07.10.2020 and 15.02.2021

DOI: 10.4213/sm9511