Extremal Quasiconformal Mappings with Free Boundary Components in Domains of Arbitray Connectivity.
Richard Fehlmann (1983)
Mathematische Zeitschrift
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Richard Fehlmann (1983)
Mathematische Zeitschrift
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Juha Heinonen (1996)
Revista Matemática Iberoamericana
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In this paper a quite complete picture is given of the absolute continuity on the boundary of a quasiconformal map B → D, where B is the unit 3-ball and D is a Jordan domain in R with boundary 2-rectifiable in the sense of geometric measure theory. Moreover, examples are constructed, for each n ≥ 3, showing that quasiconformal maps from the unit n-ball onto Jordan domains with boundary (n - 1)-rectifiable need not have absolutely continuous boundary values.
Strebel, Kurt (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
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Keiichi Shibata (1996)
Banach Center Publications
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Solutions to Beltrami differential equation with prescribed boundary correspondence in some plane domains are given.
Earle, Clifford J., Lakic, Nikola (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
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Deiermann, Paul (1993)
International Journal of Mathematics and Mathematical Sciences
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Juha Heinonen (1989)
Revista Matemática Iberoamericana
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In this paper we study quasiconformal homeomorphisms of the unit ball B = B = {x ∈ R: |x| < 1} of R onto John domains. We recall that John domains were introduced by F. John in his study of rigidity of local quasi-isometries [J]; the term John domain was coined by O. Martio and J. Sarvas seventeen years later [MS]. From the various equivalent characterizations we shall adapt the following definition based on diameter carrots, cf. [V4], [V5], [NV].
Sugawa, Toshiyuki (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
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Gutlyanskij, V.Ya., Ryazanov, V.I. (1996)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Buckley, Stephen M. (2004)
Annales Academiae Scientiarum Fennicae. Mathematica
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Vladimir Gutlyanskii, Olli Martio, Vladimir Ryazanov (2011)
Annales UMCS, Mathematica
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We give a quasiconformal version of the proof for the classical Lindelöf theorem: Let f map the unit disk D conformally onto the inner domain of a Jordan curve C. Then C is smooth if and only if arh f'(z) has a continuous extension to D. Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.
Ken’ichi Ohshika (2014)
Annales de l’institut Fourier
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We consider a quotient space of the Bers boundary of Teichmüller space, which we call the reduced Bers boundary, by collapsing each quasi-conformal deformation space lying there into a point.This boundary turns out to be independent of the basepoint, and the action of the mapping class group extends continuously to this boundary.This is an affirmative answer to Thurston’s conjecture.He also conjectured that this boundary is homeomorphic to the unmeasured lamination space by the correspondence...