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

Martin Chuaqui, Julian Gevirtz

Type: Article

Publication Date: 2003-06-12

Citations: 25

DOI: https://doi.org/10.1090/s0002-9939-03-07013-8

Abstract

We derive sharp injectivity criteria for mappings $f:(-1,1)\rightarrow \mathbb {R}^n$ in terms of Ahlforsâ definition of the Schwarzian derivative for such mappings.

Locations

Proceedings of the American Mathematical Society - View - PDF

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Works Cited by This (7)

Action	Title	Year	Authors
+	Cross-ratios and Schwarzian Derivatives in Rn	1988	Lars V. Ahlfors
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+ PDF Chat	Univalence criteria depending on the Schwarzian derivative	1979	Zeev Nehari
+ PDF Chat	The Schwarzian derivative and schlicht functions	1949	Zeev Nehari
+	Differential and Riemannian Geometry	1965	Detlef Laugwitz
+	On the Nehari univalence criterion and quasicircles	1984	F. W. Gehring Ch. Pommerenke
+	Differential and Riemannian Geometry.	1966	George F. Feeman Detlef Laugwitz Fritz Steinhardt