Tohoku Mathematical Journal

On extremal quasiconformal mappings compatible with a Fuchsian group with a dilatation bound

Ken-ichi Sakan

Full-text: Open access

Article information

Source
Tohoku Math. J. (2), Volume 37, Number 1 (1985), 79-93.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178228723

Digital Object Identifier
doi:10.2748/tmj/1178228723

Mathematical Reviews number (MathSciNet)
MR0778372

Zentralblatt MATH identifier
0566.30019

Subjects
Primary: 30C60
Secondary: 30C70: Extremal problems for conformal and quasiconformal mappings, variational methods 30F35: Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]

Citation

Sakan, Ken-ichi. On extremal quasiconformal mappings compatible with a Fuchsian group with a dilatation bound. Tohoku Math. J. (2) 37 (1985), no. 1, 79--93. doi:10.2748/tmj/1178228723. https://projecteuclid.org/euclid.tmj/1178228723


Export citation

References

  • [1] L. BERS, On moduli of Riemann surfaces, Lecture Notes, Eidgenossische Technisehe Hochschule, Zurich 1964.
  • [2] L. BERS, Automorphic forms and general Teichmller spaces, in Proc. Conf. Compl. Anal., Minneapolis, 1964, Springer-Verlag, Berlin-Heidelberg-New York, 1965, 109-113.
  • [3] L. BERS, Extremal quasiconformal mappings, in Advances in the Theory of Rieman Surfaces, Stony Brook 1969 (Ed. by L. V. Ahlfors et al.), Ann. of Math. Studies 66, Princeton Univ. Press, 1971, 27-52.
  • [4] L. BERS, A new proof of a fundamental inequality for quasiconformal mappings, J. Analyse Math. 36 (1979), 15-30.
  • [5] C. J. EARLE, Teichmller spaces of groups of the second kind, Acta Math. 112 (1964), 91-97
  • [6] C. J. EARLE, Reduced Teichmller spaces, Trans. Amer. Math. Soc. 126 (1967), 54-6
  • [7] R. FEHLMANN, Ueber extremale quasikonforme Abbildungen, Comment. Math. Helv. 5 (1981), 558-580.
  • [8] R. FEHLMANN, On absolutely extremal quasiconformal mappings, University of Minnesota, Mathematics Report 81-146.
  • [9] F. P. GARDINER, The existence of Jenkins-Strebel diferentials from Teichmller theory, Amer. J. Math. 99 (1975), 1097-1104.
  • [10] F. P. GARDINER, On the variation of Teichmller's metric, Proc. Roy. Soc. Edinburg Sect. A 85 (1980), 143-152.
  • [11] F. P. GARDINER, On partially Teichmller Beltrami differentials, Michigan Math. J. 2 (1982), 237-242.
  • [12] O. LEHTO AND K. I. VIRTANEN, Quasiconformal mappings in the plane, Springer-Verlag, Berlin-Heidelberg-New York, 1973.
  • [13] E. REICH AND K. STREBEL, On quasiconformal mappings which keep the boundary point fixed, Trans. Amer. Math. Soc. 138 (1969), 211-222.
  • [14] E. REICH AND K. STREBEL, Extremal quasiconformal mappings with given boundar values, in Contributions to Analysis, A Collection of Papers Dedicated to Lipman Bers, Academic Press, New York, 1974, 375-391.
  • [15] E. REICH, On the relation between local and global properties of boundary values fo extremal quasiconformal mappings, in Discontinuous Groups and Riemann Surfaces, Univ. of Maryland, 1973 (Ed. by L. Greenberg), Ann. of Math. Studies 79, Princeton Univ. Press, 1974, 391-407.
  • [16] E. REICH, Quasiconformal mappings with prescribed boundary values and a dilatatio bound, Arch. Rational Mech. Anal. 68 (1978), 99-112.
  • [17] K. SAKAN, On extremal quasiconformal mappings compatible with a Fuchsian group, Thoku Math. J. 34 (1982), 87-100.
  • [18] K. STREBEL, Ein Konvergenzsatz fur Folgen quasikonformer Abbildungen, Comment Math. Helv. 44 (1969), 469-475.
  • [19] K. STREBEL, On the existence of extremal Teichmuller mappings, J. Analyse Math. 3 (1976), 464-480.
  • [20] K. STREBEL, On quasiconformal mappings of open Riemann surfaces, Comment. Math Helv. 53 (1978), 301-321.