J. E. McMillan's Area theorem
Michael O'Neill (1999)
Colloquium Mathematicae
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Displaying similar documents to “Conformal welding of Jordan curves using weighted Dirichlet spaces.”
J. E. McMillan's Area theorem
What is a disk?
Kari Hag (1999)
Banach Center Publications
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This paper should be considered as a companion report to F.W. Gehring’s survey lectures “Characterizations of quasidisks” given at this Summer School [7]. Notation, definitions and background results are given in that paper. In particular, D is a simply connected proper subdomain of unless otherwise stated and D* denotes the exterior of D in . Many of the characterizations of quasidisks have been motivated by looking at properties of euclidean disks. It is therefore natural to go...
Quasi-conformal mappings in -space and the rigidity of hyperbolic space forms
G. D. Mostow (1968)
Publications Mathématiques de l'IHÉS
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Extension of internally bilipschitz maps in John disks.
Broch, Ole Jacob (2006)
Annales Academiae Scientiarum Fennicae. Mathematica
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Some homeomorphisms of the sphere conformal off a curve.
Bishop, Christopher J. (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Characterizations of quasidisks
Frederick Gehring (1999)
Banach Center Publications
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John disks and the pre-Schwarzian derivative.
Hag, Kari, Hag, Per (2001)
Annales Academiae Scientiarum Fennicae. Mathematica
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Reflection and the Dirichlet problem on doubly connected regions
Eva Dontová (1988)
Časopis pro pěstování matematiky
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On a theorem of Haimo regarding concave mappings
Martin Chuaqui, Peter Duren, Brad Osgood (2011)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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A relatively simple proof is given for Haimo’s theorem that a meromorphic function with suitably controlled Schwarzian derivative is a concave mapping. More easily verified conditions are found to imply Haimo’s criterion, which is now shown to be sharp. It is proved that Haimo’s functions map the unit disk onto the outside of an asymptotically conformal Jordan curve, thus ruling out the presence of corners.
On a question of T. Sheil-Small regarding valency of harmonic maps
Daoud Bshouty, Abdallah Lyzzaik (2012)
Annales UMCS, Mathematica
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The aim of this work is to answer positively a more general question than the following which is due to T. Sheil-Small: Does the harmonic extension in the open unit disc of a mapping f from the unit circle into itself of the form f(eit) = eiϕ(t), 0 ≤ t ≤ 2π, where ϕ is a continuously non-decreasing function that satisfies ϕ(2π)−ϕ(0) = 2Nπ, assume every value finitely many times in the disc?