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- W1580879905 abstract "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 quasi- conformal extensions. The extension is obtained by a reflection across the boundary of the surface using a family of Euclidean circles orthogonal to the surface. This gives a geometric generalization of the Ahlfors-Weill formula and extends the minimal surface. Thus one obtains a homeomorphism of C onto a toplological sphere in R3 = R 3 ( {1} that is real-analytic off the boundary. The hypotheses involve bounds on a generalized Schwarzian derivative for harmonic mappings in term of the hyperbolic metric of the disk and the Gaussian curvature of the minimal surface. Hyperbolic convexity plays a crucial role." @default.
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- W1580879905 date "2010-05-26" @default.
- W1580879905 modified "2023-09-27" @default.
- W1580879905 title "AHLFORS-WEILL EXTENSIONS FOR A CLASS OF MINIMAL SURFACES" @default.
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