Displaying similar documents to “Several theorems concerning extensions of meromorphic and conformal mappings”

On a theorem of Haimo regarding concave mappings

Martin Chuaqui, Peter Duren, Brad Osgood (2011)

Annales UMCS, 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 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.

Real commutative algebra. III. Dedekind-Weber-Riemann manifolds.

D. W. Dubois, A. Bukowski (1980)

Revista Matemática Hispanoamericana

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The space S of all non-trivial real places on a real function field K|k of trascendence degree one, endowed with a natural topology analogous to that of Dedekind and Weber's Riemann surface, is shown to be a one-dimensional k-analytic manifold, which is homeomorphic with every bounded non-singular real affine model of K|k. The ground field k is an arbitrary ordered, real-closed Cantor field (definition below). The function field K|k is thereby represented as a field of real mappings...