Ukrainian Mathematical Bulletin
Volume 4, Issue 2, 2007 pp. 199-233.
Weakly Flat Spaces and Boundaries in the Mapping TheoryAuthors: Vladimir I. Ryazanov, Ruslan R. Salimov
Author institution: Institute of Applied Mathematics and Mechanics NAS of Ukraine ul. Roze Luxemburg, 74, Donetsk, 83114, Ukraine ryazanov@iamm.ac.donetsk.ua, salimov@iamm.ac.donetsk.ua
Summary: We study the problem of continuation to the boundary of the so-called $Q$-homeomorphisms between domains in metric spaces with measures. We formulate conditions on the function $Q(x)$ and the boundary of the domain such that every $Q$-homeomorphism admits a continuous or homeomorphic continuation to the boundary. The results can be applied to Riemann manifolds, Loewner spaces, Carnot groups, and Heisenberg groups.
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