Simple curves in $\mathbb {R}^n$ and Ahlfors’ Schwarzian derivative

DOI10.1090/S0002-9939-03-07013-8zbMath1045.53003MaRDI QIDQ4429724

Julian Gevirtz, Martin Chuaqui Farrú

Publication date: 28 September 2003

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Schwarzian derivativeinjectivitycurveNehari criteria

Mathematics Subject Classification ID

Curves in Euclidean and related spaces (53A04) Differential invariants (local theory), geometric objects (53A55) General theory of univalent and multivalent functions of one complex variable (30C55)

Related Items (12)

Injectivity of minimal immersions and homeomorphic extensions to space ⋮ Quasiconformal extensions to space of Weierstrass-Enneper lifts ⋮ Univalence criteria for lifts of harmonic mappings to minimal surfaces ⋮ Two-point distortion theorems for harmonic mappings ⋮ Schwarzian derivatives and uniform local univalence ⋮ Integral conditions on the Schwarzian for curves to be simple or unknotted ⋮ General criteria for curves to be simple ⋮ An Ahlfors derivative for conformal immersions ⋮ Schwarzian derivative criteria for valence of analytic and harmonic mappings ⋮ Quasiconformal extensions of harmonic mappings ⋮ On Ahlfors' imaginary Schwarzian ⋮ Uniform domains on holomorphic curves

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