Open AccessQuasi-isometric extensions of quasisymmetric mappings of the real line compatible with composition
Author(s) -
Zair Ibragimov
Publication year - 2010
Publication title -
annales academiae scientiarum fennicae mathematica
Language(s) - English
Resource type - Journals
eISSN - 1798-2383
pISSN - 1239-629X
DOI - 10.5186/aasfm.2010.3513
Subject(s) - isometric exercise , composition (language) , mathematics , line (geometry) , computer science , linguistics , medicine , philosophy , geometry
We show that it is possible to extend, in a homomorphic fashion, each quasisym- metric homeomorphism of the real line to a quasi-isometry of the upper-half plane. Epstein and Markovic have recently shown that a homomorphic extension to quasiconformal homeomorphisms of the upper-half plane is not possible.
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