Modulus Characterizations of Bilipschitz Mappings

Qingshan Zhou, Zhiqiang Yang, Antti Rasila, Yuehui He*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, we establish six necessary and sufficient conditions for a homeomorphism of Rn onto itself to be strongly quasisymmetric. These conditions are quantitative in terms of conformal moduli of disjoint continua as well as the geometric modulus, which was recently introduced by Tukia and Väisälä. Note that all of them are equivalent to bilipschitz continuity with parameters depending also on two fixed points. As an application, we obtain several quantitative characterizations for a homeomorphism of the Riemann sphere R¯n onto itself to be strongly quasimöbius.

Original languageEnglish
Article number155
JournalJournal of Geometric Analysis
Issue number6
StatePublished - Jun 2024


  • Bilipschitz mapping
  • Geometric modulus
  • Modulus
  • Ring
  • Strongly quasimöbius mapping
  • Strongly quasisymmetric mapping


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