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Length of curves under conformal mappings

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Commentarii Mathematici Helvetici

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References

  1. Ahlfors, L. V.,Conformal Invariants, McGraw Hill, New York, (1973).

    MATH  Google Scholar 

  2. —,Lectures on quasiconformal mapping, Van Nostrand, Princeton, (1966).

    Google Scholar 

  3. Belna, C., Cohn, W., Piranian, G. andStephenson, K.,Level sets of special Blaschke products, Michigan Math. J.29 (1982), 79–81.

    Article  MathSciNet  Google Scholar 

  4. Collingwood, E. F. andLohwater, A. J.,Theory of Cluster Sets, Cambridge University Press, (1966).

  5. Flinn, B. B.,Hyperbolic Convexity and Level Sets of Analytic Functions, Indiana Math. J.32(6) (1983), 831–841.

    Article  MathSciNet  Google Scholar 

  6. Garnett, J. B.,Bounded Analytic Functions, Academic Press, New York, (1981).

    MATH  Google Scholar 

  7. Garnett, J. F., Gehring, F. W. andJones, P. W.,Conformal invariant length sums, Indiana Math. J.32(6) (1983) 809–829.

    Article  MathSciNet  Google Scholar 

  8. Hayman, W. K. andWu, J. M.,Level sets of univalent functions, Comment Mat. Helv.56 (1981), 366–403.

    MathSciNet  Google Scholar 

  9. Jerison, D. andKenig, C. Boundary behaviour of harmonic functions in non-tangentially accessible domains, Advances in Math.46 (1982) 80–147.

    Article  MathSciNet  Google Scholar 

  10. Kaufman, R. andWu, J. M.,Distortion of the boundary under conformal mapping, Mich. Math. J.29 (1982), 267–280.

    Article  MathSciNet  Google Scholar 

  11. Martio, O. andSarvas, J.,Injectivity theorems in the plane and space, Ann. Acad. Sci. Fenn. Ser. AI. Math.4 (1979), 383–401.

    MathSciNet  Google Scholar 

  12. Pommerenke, C.,Boundary behaviour of conformal mapping, inAspects of Contemporary Complex Analysis, edited by Brannan, D. and Clunie, J., Academic Press, New York, 1980.

    Google Scholar 

  13. Sullivan, D.,The density at infinity of a discrete group of hyperbolic motions, Publ. IHES50 (1979), 419–450.

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Mathematics, University of Maryland, 20742, College Park, Maryland, USA

    José L. Fernández & David H. Hamilton

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  1. José L. Fernández
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  2. David H. Hamilton
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Research supported in part by NSF Grants 8120790 and 8501509.

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Fernández, J.L., Hamilton, D.H. Length of curves under conformal mappings. Commentarii Mathematici Helvetici 62, 122–134 (1987). https://doi.org/10.1007/BF02564441

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