Quasiconformal images of Hölder domains.
Buckley, Stephen M. (2004)
Annales Academiae Scientiarum Fennicae. Mathematica
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Buckley, Stephen M. (2004)
Annales Academiae Scientiarum Fennicae. Mathematica
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Herron, David A., Koskela, Pekka (1995)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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José L. Fernandez (1989)
Revista Matemática Iberoamericana
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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].
Väisälä, Jussi (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Stefan Bergman (1977)
Annales Polonici Mathematici
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Brian D. Sleeman, Chen Hua (2000)
Revista Matemática Iberoamericana
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A fundamental question raised by M. Kac in 1966 is: Must two isospectral planar domains necessarily be isometric? Following a long history of investigation C. Gordon, D. L. Webb and S. Wolpert in 1992 finally proved that the answer is no. By using the idea of transposition maps one can construct a wide class of planar domains with piecewise continuous boundaries which are isospectral but non-isometric. In this note we study the Kac question in relation to domains with fractal boundaries...
McCarthy, John, Papadopoulos, Athanase (1996)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Roberto Peirone (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We state that in opportune tubular domains any two points are connected by a bounce trajectory and that there exist non-trivial periodic bounce trajectories.
Mark Comerford (2014)
Open Mathematics
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We continue our exposition concerning the Carathéodory topology for multiply connected domains which we began in [Comerford M., The Carathéodory topology for multiply connected domains I, Cent. Eur. J. Math., 2013, 11(2), 322–340] by introducing the notion of boundedness for a family of pointed domains of the same connectivity. The limit of a convergent sequence of n-connected domains which is bounded in this sense is again n-connected and will satisfy the same bounds. We prove a result...
Roberto Peirone (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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We state that in opportune tubular domains any two points are connected by a bounce trajectory and that there exist non-trivial periodic bounce trajectories.
Harjulehto, Petteri (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
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