Skip to main content
Log in

Unique extremality

  • Published:
Journal d’Analyse Mathématique Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • [A] L. Ahlfors,Finitely generated Kleinian groups, Amer. J. Math.86 (1964), 413–429;87 (1965), 759.

    Article  MathSciNet  Google Scholar 

  • [B] L. Bers,An approximation theorem, J. Analyse Math.,14 (1965) 1–4.

    MATH  MathSciNet  Google Scholar 

  • [BA] A. Beurling and L. Ahlfors,The boundary correspondence under quasiconformal mappings, Acta Math.,96 (1956), 125–142.

    Article  MATH  MathSciNet  Google Scholar 

  • [BR] L. Bers and H. L. Royden,Holomorphic families of injections, Acta Math.157 (1986), 259–286.

    Article  MATH  MathSciNet  Google Scholar 

  • [EKK] C. J. Earle, I. Kra and S. L. Krushkal,Holomorphic motions and Teichmüller spaces, Trans. Amer. Math. Soc.,343 (1994), 927–948.

    Article  MATH  MathSciNet  Google Scholar 

  • [EG] C. J. Earle and F. P. Gardiner,Geometric isomorphisms between infinite dimensional Teichmüller spaces, Trans. Amer. Math. Soc.348 (1996), 1163–1190.

    Article  MATH  MathSciNet  Google Scholar 

  • [EGL] C. J. Earle, F. P. Gardiner and N. Lakic,Vector fields for holomorphic motions of closed sets, Contemp. Math.211 (1997), 193–225.

    MathSciNet  Google Scholar 

  • [ELa] C. J. Earle and N. LakicVariability set on a Riemann surface, preprint.

  • [EL] C. J. Earle and Zhong Li,Isometrically embedded polydisks in infinite dimensional Teichmüller spaces, J. Geom. Anal., to appear.

  • [EL2] C. J. Earle and Zhong Li,Extremal quasiconformal mappings, preprint.

  • [G] F. P. Gardiner,Teichmüller Theory and Quadratic Differentials, Wiley-Interscience, New York, 1987.

    MATH  Google Scholar 

  • [Gr] H. Grötzsch,Über die Verzerrung bei schlichten nicht konformen Abbildungen und über eine damit zusammenhängende Erweiterung des Picardschen Satzes, Ber. Verh. Sächs. Akad. Wiss. Leipzig80 (1928), 503–507.

    Google Scholar 

  • [H] R. S. Hamilton,Extremal quasiconformal mappings with prescribed boundary values, Trans. Amer. Math. Soc.,138 (1969), 399–406.

    Article  MATH  MathSciNet  Google Scholar 

  • [K] S. Krushkal,Extremal, quasiconformal mappings, Siberian Math. J.10 (1969), 411–418.

    Article  MATH  Google Scholar 

  • [Kr] I. Kra,Automorphic Forms and Kleinian Groups, Benjamin, Reading, Massachusetts, 1972.

    MATH  Google Scholar 

  • [L1] N. Lakic,Strebel points, Contemp. Math.211 (1997), 417–431.

    MathSciNet  Google Scholar 

  • [L2] N. Lakic,Infinitesimal, Teichmüller geometry, Complex Variables Theory Appl.30 (1996), 1–17.

    MATH  MathSciNet  Google Scholar 

  • [Li] G. S. Lieb,Holomorphic motions and Teichmüller space, Ph.D. Thesis, Cornell Univ., 1990.

  • [Liz] Zhong Li,Nonuniqueness of geodesics in infinite dimensional Teichmüller spaces, Complex Variables Theory Appl.16 (1991), 261–272.

    MATH  MathSciNet  Google Scholar 

  • [MM] M. Mateljević and V. Marković,The unique extremal q.c. mappings and uniqueness of Hahn-Banach extension, Matematichki Vesnik48 (1996), 107–112.

    MathSciNet  MATH  Google Scholar 

  • [P] M. Pavlovic, in preparation.

  • [R1] E. Reich,On criteria for unique extremality of Teichmüller mappings, Ann. Acad. Sci. Fenn. Ser. A I Math.,6 (1981), 289–301.

    MathSciNet  MATH  Google Scholar 

  • [R2] E. Reich,Extremal extensions from the circle to the disk, preprint.

  • [R3] E. Reich,On the uniqueness question for Hahn-Banach extensions from the space of L 1 analytic functions, Proc. Amer. Math. Soc.88 (1983), 305–310.

    Article  MATH  MathSciNet  Google Scholar 

  • [R4] E. Reich,On criteria for unique extremality of Teichmüller mappings, Indiana Univ. Math. J.30 (1981), 441–447.

    Article  MATH  MathSciNet  Google Scholar 

  • [R5] E. Reich,An extremum problem for analytic functions with area norm, Ann. Acad. Sci. Fenn. Ser. A I Math.2 (1976), 429–445.

    MathSciNet  MATH  Google Scholar 

  • [RS] E. Reich and K. Strebel,Extremal quasiconformal mappings with given boundary values, inContributions to Analysis (L. Ahlfors et al., eds.), Academic Press, New York, 1974, pp. 375–392.

    Google Scholar 

  • [RS2] E. Reich and K. Strebel,On the extremality of certain Teichmüller mappings, Comment. Math. Helv.45 (1970), 353–362.

    Article  MATH  MathSciNet  Google Scholar 

  • [S1] Z. Slodkowski,Holomorphic motions and polynomial hulls, Proc. Amer. Math. Soc.111 (1991), 347–355.

    Article  MATH  MathSciNet  Google Scholar 

  • [S1] K. Strebel,On quasiconformal mappings of open Riemann surfaces, Comment. Math. Helv.53 (1978), 301–321.

    Article  MATH  MathSciNet  Google Scholar 

  • [S2] K. Strebel,On the existence of extremal Teichmüller mappings, J. Analyse Math.30 (1976), 464–480.

    Article  MATH  MathSciNet  Google Scholar 

  • [S3] K. Strebel,Eine abschätzung der länge gewisser kurven bei quasikonformer Abbildung, Ann. Acad. Sci. Fenn.,243 (1957), 1–10.

    MathSciNet  Google Scholar 

  • [S4] K. Strebel,Zur frage der eindeutigkeit extremaler quasikonformer abbildungen des einheitskreises I and II, Comment. Math. Helv.36 (1962), 306–323;39 (1964), 77–89.

    Article  MATH  MathSciNet  Google Scholar 

  • [S5] K. Strebel,Quadratic Differentials, Springer-Verlag, Berlin and New York, 1984.

    MATH  Google Scholar 

  • [T] O. Teichmüller,Extremale quasikonforme abbildungen und quadratische differentiale, Abh. Preuss Akad. Wiss., Math.-Natur. Kl.22 (1939), 1–197.

    Google Scholar 

  • [Y] S. Yu-Liang,On the weak convexity of Q(R), Proc. Amer. Math. Soc.,124 (1996), 1879–1882.

    Article  MathSciNet  Google Scholar 

  • [Z] Zhong Li,Nonuniqueness of, geodesics in infinite dimensional Teichmüller spaces, Complex Variables Theory Appl.16 (1991), 261–272.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. Božin.

Additional information

Research of the second author supported in part by NSF grant DMS 9706769.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Božin, V., Lakic, N., Marković, V. et al. Unique extremality. J. Anal. Math. 75, 299–338 (1998). https://doi.org/10.1007/BF02788704

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02788704

Keywords

Navigation