Anatoly Golberg (Bar-Ilan University)
Distortion properties of generalized quasiconformal
mappings
Abstract.
In the talk we consider homeomorphisms whose dilatations are bounded in
certain integral sense. The resulting notion generalizes quasiconformal
mappings, mappings quasiconformal in the mean and other classes of
homeomorphic mappings. Such mappings naturally arise, for example, by
transforming $k$-dimensional surfaces on $n$-dimensional manifolds with
$n > k$ under special rules. The main method for investigation is based
on appropriate variation of certain geometric quantities and involves
some intrinsically related systems of the closed neighborhoods of a
point. This approach allows us to estimate the distortion of distances
under such mappings. Another application consists of generalizing the
classical Menshov theorem on homeomorphic mappings preserving
infinitesimal circles.
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