Zobrazeno 1 - 10
of 166
pro vyhledávání: '"Duren, Peter"'
We derive a quasiconformal extension to 3-space of the Weierstrass-Enneper lifts of a class of harmonic mappings defined in the unit disk. The extension is based on fibrations of space by circles in domain and image that correspond to each other in a
Externí odkaz:
http://arxiv.org/abs/1304.4198
In earlier work the authors have extended Nehari's well-known Schwarzian derivative criterion for univalence of analytic functions to a univalence criterion for canonical lifts of harmonic mappings to minimal surfaces. The present paper develops some
Externí odkaz:
http://arxiv.org/abs/1005.5333
The Ahlfors-Weill extension of a conformal mapping of the disk is generalized to the lift of a harmonic mapping of the disk to a minimal surface, producing homeomorphic and quasiconformal extensions. The extension is obtained by a reflection across t
Externí odkaz:
http://arxiv.org/abs/1005.4937
Quantitative estimates are obtained for the (finite) valence of functions analytic in the unit disk with Schwarzian derivative that is bounded or of slow growth. A harmonic mapping is shown to be uniformly locally univalent with respect to the hyperb
Externí odkaz:
http://arxiv.org/abs/0706.4296