A new intrinsic metric and quasiregular maps

Abstract

We introduce a new intrinsic metric in subdomains of a metric space and give upper and lower bounds for it in terms of well-known metrics. We also prove distortion results for this metric under quasiregular maps.

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Acknowledgements

This work was partially supported by JSPS KAKENHI Grant No. 19K03531 and by JSPS Grant BR171101.

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Correspondence to Masayo Fujimura.

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Dedicated to Professor Pekka Koskela on the occasion of his sixtieth birthday.

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Fujimura, M., Mocanu, M. & Vuorinen, M. A new intrinsic metric and quasiregular maps. Complex Anal Synerg 7, 6 (2021). https://doi.org/10.1007/s40627-021-00066-z

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Keywords

  • Hyperbolic metric
  • Triangular ratio metric
  • Quasiconformal map
  • Quasiregular map

Mathematics Subject Classification

  • 30C20
  • 30C15
  • 51M99