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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