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Articles

Uniform domains on holomorphic curves

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Pages 1015-1031 | Received 11 Jul 2014, Accepted 19 Nov 2014, Published online: 12 Jan 2015

References

  • Chuaqui M, Duren P, Osgood B. Univalence criteria for lifts of harmonic mappings to minimal surfaces. J. Geomet. Anal. 2007;17:49–74.
  • Chuaqui M, Duren P, Osgood B. Injectivity criteria for holomorphic curves in ℂn. Pure Appl. Math. Q. 2011;7:223–251.
  • Nehari Z. Some criteria of univalence. Proc. Am. Math. Soc. 1954;5:700–704.
  • Gehring FW, Pommerenke Ch. On the Nehari univalence criterion and quasicircles. Comment. Math. Helv. 1984;59:226–242.
  • Ahlfors LV. Cross-ratios and Schwarzian derivatives in ℝn, Complex analysis. Basel: Birkhäuser; 1988. p. 1–15.
  • Chuaqui M, Gevirtz J. Simple curves in ℝn and Ahlfors’ Schwarzian derivative. Proc. Am. Math. Soc. 2004;132:223–230.
  • Stowe D. An Ahlfors derivative for conformal immersions. J. Geomet. Anal. 2013. in press (available on-line).
  • Ahlfors LV, Weill G. A uniqueness theorem for Beltrami equations. Proc. Am. Math. Soc. 1962;13:975–978.
  • Sierra W. John surfaces associated with a class of harmonic mappings. Ann. Acad. Sci. Fenn-Math. 2013;38:595–616.
  • Chuaqui M, Duren P, Osgood B. Quasiconformal extensions to space of Weierstrass–Enneper lifts. Arxiv preprint 1304.4198.
  • Chuaqui M, Osgood B. Ahlfors–Weill extensions of conformal mappings and critical points of the Poincaré metric. Comment. Math. Helv. 1994;69:659–668.
  • Gehring FW, Osgood B. Uniform domains and the quasi-hyperbolic metric. J. Anal. Math. 1980;36:50–74.
  • Chuaqui M, Osgood B. Sharp distortion theorems associated with the Schwarzian derivative. J. London Math. Soc. 1993;48:289–298.
  • Chuaqui M, Duren P, Osgood B. Two-point distortion theorems for harmonic mappings. Illinois J. Math. 2009;53:1061–1075.

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