On BLD-mappings with small distortion

Abstract

We show that every \(L\)-BLD-mapping in a domain of \(\mathbb {R}^{n}\) is a local homeomorphism if \(L < \sqrt{2}\) or \(K_I(f) < 2\). These bounds are sharp as shown by a winding map.

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Correspondence to Rami Luisto.

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Dedicated to Professor Pekka Koskela on his 59th birthday.

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A.K. acknowledges the support of Academy of Finland, Grant Number 322441

The research of V.T. was supported by the Academy of Finland, Project Number 308759.

R.L. was partially supported by the Academy of Finland (grant 288501 ‘Geometry of subRiemannian groups’) and by the European Research Council (ERC Starting Grant 713998 GeoMeG ‘Geometry of Metric Groups’)

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Kauranen, A., Luisto, R. & Tengvall, V. On BLD-mappings with small distortion. Complex Anal Synerg 7, 5 (2021). https://doi.org/10.1007/s40627-021-00067-y

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Keywords

  • BLD-mappings
  • branch set
  • quasiregular mappings
  • local homeomorphism

Mathematics Subject Classification

  • 57M12
  • 30C65