Ukrainian Mathematical Bulletin

Volume 1, Issue 3, 2004 pp. 353-376.

Relative Distance of Lavrent'eff and Prime Ends on Nonparametric Surfaces

Authors: Vladimir M. Miklyukov
Author institution: Volgograd State University, 2nd Prodolnaya Str., 30, Volgograd 400062, Russia

Summary: $Q^*$-homeomorphisms of locally Lipschitz nonparametric surfaces are considered. Some estimates of a Lavrent'eff relative distance are proved. Applications to the theory of prime ends on surfaces are given. In particular, we prove that introduced prime ends are invariant under conformal mappings from surfaces onto surfaces and give some estimates of the relative distance.

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