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Bi-Lipschitz Property of HQC Mappings

  • Vesna Todorčević
Chapter
  • 180 Downloads

Abstract

The inverse of a K-quasiconformal homeomorphism is also K-quasiconformal. By the Schwarz lemma for K-quasiconformal mappings we know that both mappings are Hölder continuous in the Euclidean metric with exponent K1∕(1−n), and the Gehring–Osgood result yields the same conclusion in the quasihyperbolic metric. The class of harmonic K-quasiconformal interpolates between the classes of conformal maps and general quasiconformal maps. In this chapter we study the modulus of continuity of harmonic quasiconformal mappings relative to the quasihyperbolic metric and prove that both the mapping and its inverse are Lipschitz-continuous.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Vesna Todorčević
    • 1
    • 2
  1. 1.Faculty of Organizational SciencesUniversity of BelgradeBelgradeSerbia
  2. 2.Mathematical InstituteSerbian Academy of Sciences and ArtsBelgradeSerbia

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