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Homeomorphisms of Finite Metric Distortion Between Riemannian Manifolds

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Abstract

The theory of multidimensional quasiconformal mappings employs three main approaches: analytic, geometric (modulus) and metric ones. In this paper, we use the last approach and establish the relationship between homeomorphisms of finite metric distortion (FMD-homeomorphisms), finitely bi-Lipschitz, quasisymmetric and quasiconformal mappings on Riemannian manifolds. One of the main results shows that FMD-homeomorphisms are lower Q-homeomorphisms. As an application, there are obtained some sufficient conditions for boundary extensions of FMD-homeomorphisms. These conditions are illustrated by several examples of FMD-homeomorphisms.

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Acknowledgements

The authors cordially thank Pekka Koskela for useful ideas and valuable remarks concerning our manuscript which essentially have improved its presentation. We also would like to thank the referee for carefully checking the manuscript and for making useful suggestions.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, 1 Dobrovol’skogo St., Slavyansk, 84100, Ukraine

    Elena Afanas’eva

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

    Anatoly Golberg

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  1. Elena Afanas’eva
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  2. Anatoly Golberg
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Correspondence to Anatoly Golberg.

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Communicated by Pekka Koskela.

Dedicated to Pekka Koskela on the occasion of his 60th birthday.

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Afanas’eva, E., Golberg, A. Homeomorphisms of Finite Metric Distortion Between Riemannian Manifolds. Comput. Methods Funct. Theory 22, 755–780 (2022). https://doi.org/10.1007/s40315-021-00431-3

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  • DOI: https://doi.org/10.1007/s40315-021-00431-3

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