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Regularity of Mappings with Integrally Restricted Moduli

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Complex Analysis and Dynamical Systems

Part of the book series: Trends in Mathematics ((TM))

Abstract

We consider certain classes of homeomorphisms of domains in \(\mathbb R^n\) with integrally bounded p-moduli of the families of curves and surfaces, which essentially extend the well-known classes of mappings such as quasiconformal, quasiisometric, Lipschitzian, etc. In the paper we survey the known results in this field regarded to the differential properties of such homeomorphisms, but mainly present a wide range of open related problems.

Dedicated to the memory of Sasha Vasil’ev

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Acknowledgement

The first author was supported by EU FP7 IRSES program STREVCOMS, grant no. PIRSES-2013-612669.

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Authors and Affiliations

  1. Department of Mathematics, Holon Institute of Technology, 52 Golomb St., P.O.B. 305, Holon, 5810201, Israel

    Anatoly Golberg

  2. Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkivska St., Kiev-4, 01601, Ukraine

    Ruslan Salimov

Authors
  1. Anatoly Golberg
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  2. Ruslan Salimov
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Corresponding author

Correspondence to Anatoly Golberg .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

    Mark Agranovsky

  2. Department of Mathematics, Holon Institute of Technology, Holon, Israel

    Anatoly Golberg

  3. Department of Mathematics, ORT Braude College, Karmiel, Israel

    Fiana Jacobzon

  4. Department of Mathematics, Holon Institute of Technology, Holon, Israel

    David Shoikhet

  5. Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

    Lawrence Zalcman

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Golberg, A., Salimov, R. (2018). Regularity of Mappings with Integrally Restricted Moduli. In: Agranovsky, M., Golberg, A., Jacobzon, F., Shoikhet, D., Zalcman, L. (eds) Complex Analysis and Dynamical Systems. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-70154-7_8

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