Mappings with integrally controlled moduli: regularity properties

יום ב', 11/12/2017 - 14:00
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Abstract: 

We consider the classes of homeomorphisms of domains in $\mathbb R^n$ with $p$-moduli
of the families of curves and surfaces integrally bounded from above and below. These
classes essentially extend the well-known classes of mappings such as quasiconformal,
quaiisometric, Lipschitzian, etc.
In the talk, we survey the known results in this field but mainly establish new differential
properties of such mappings. A collection of related open problems will also be presented.