Displaying similar documents to “John disks and the pre-Schwarzian derivative.”

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.

Generalized John disks

Chang-Yu Guo, Pekka Koskela (2014)

Open Mathematics

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We establish the basic properties of the class of generalized simply connected John domains.

On a theorem of Haimo regarding concave mappings

Martin Chuaqui, Peter Duren, Brad Osgood (2011)

Annales UMCS, Mathematica

Similarity:

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.

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 R 2 unless otherwise stated and D* denotes the exterior of D in R ¯ 2 . Many of the characterizations of quasidisks have been motivated by looking at properties of euclidean disks. It is therefore natural to go...