Bi-Sobolev Extensions

Aleksis Koski, Jani Onninen

Research output: Contribution to journalArticlepeer-review


We give a full characterization of circle homeomorphisms which admit a homeomorphic extension to the unit disk with finite bi-Sobolev norm. As a special case, a bi-conformal variant of the famous Beurling–Ahlfors extension theorem is obtained. Furthermore we show that the existing extension techniques such as applying either the harmonic or the Beurling–Ahlfors operator work poorly in the degenerated setting. This also gives an affirmative answer to a question of Karafyllia and Ntalampekos.

Original languageEnglish (US)
Article number301
JournalJournal of Geometric Analysis
Issue number9
StatePublished - Sep 2023


  • Beurling–Ahlfors extension
  • Harmonic extension
  • Quasiconformal mapping and mapping of finite distortion
  • Sobolev extensions
  • Sobolev homeomorphisms

ASJC Scopus subject areas

  • Geometry and Topology


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