This is a preview of subscription content, log in via an institution to check access.
References
V. M. Gol'dshtein and Yu. G. Reshetnyak, Quasiconformal Mappings and Sobolev Spaces, Kluwer, Dordrecht (1990).
V. M. Gol'dshtein and S. K. Vodop'yanov, “Structural isomorphisms of the spacesW 1,n and quasiconformal mappings," Sibirsk. Mat. Zh.,16, 768–773 (1975).
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin (1983).
R. Hurri, "Poincaré domains inR n,” Ann. Acad. Sci. Fenn. Ser. A I Math. Diss.,71 (1988).
D. H. Hamilton, “On the Poincaré inequality,” Complex Variables,5, 265–270 (1986).
W. Smith and D. A. Stegenga, “Poincaré domains in the plane,” in: Proc. 13th Rolf Nevanlinna Colloq. (Lecture Notes in Math.,1351), Springer, Berlin, 1988, pp. 312–327.
W. Smith and D. A. Stegenga, “Hölder domains and Poincaré domains,” Trans. Amer. Math. Soc.,319, 67–100 (1990).
A. D. Herron and P. Koskela, “Uniform, Sobolev extension and quasiconformal circle domains,” J. Analyse Math.,57, 172–202 (1991).
S. Axler and A. L. Shields, “Univalent multipliers of the Dirichlet space,” Michigan Math. J.,32, 65–80 (1985).
F. W. Gehring and O. Martio, “Quasiextremal distance domains and extendability of quasiconformal mappings,” J. Analyse Math.,45, 181–206 (1985).
D. A. Herron and P. Koskela, “Uniform and Sobolev extension domains,” Proc. Amer. Math. Soc.,114, 483–489 (1992).
V. G. Maz'ja, Sobolev Spaces, Springer, Berlin (1985).
J. VÄisÄlÄ, Lectures onn-Dimensional Quasiconformal Mappings, Springer, Berlin etc. (1971). (Lecture Notes in Math.;229.)
S. K. Vodop'yanov, “L p potential theory and quasiconformal mappings on homogeneous groups,” in: Modern Problems of Geometry and Analysis [in Russian], Trudy Inst. Mat. Vol. 14 (Novosiirsk), Nauka, Novosibirsk, 1989, pp. 45–89.
P. W. Jones, “Quasiconformal mappings and extendability of functions in Sobolev spaces,” Acta Math.,147, 71–88 (1981).
V. M. Gol'dshtein, T. G. Latfullin, and S. K. Vodop'yanov, “Criteria for extension of functions of the classL 12 from unbounded plane domains,” Sibirsk. Mat. Zh.,20, 298–301 (1979).
M. Vuorinen, Conformal Geometry and Quasiregular Mappings, Springer, Berlin etc. (1988). (Lecture Notes in Math.,1319.)
T. Iwaniec and R. Kosecki, “Sharp estimates for complex potentials and quasiconformal mappings,” Manuscript.
J. Hesse, “Ap-extremal length andp-capacity inequality,” Ark. Mat.,13 131–144 (1975).
P. Koskela, “Capacity extension domains,” Ann. Acad. Sci. Fenn. Ser. A I Math. Diss.,73 (1990).
F. W. Gehring and J. VÄisÄlÄ, “The coefficients of quasiconformality of domains in space,” Acta Math.,114, 1–70 (1965).
S. K. Vodop'yanov, “Mappings of homogeneous groups and embeddings of function spaces,” Sibirsk. Mat. Zh.,30, 685–698 (1990).
Author information
Authors and Affiliations
Additional information
The second author is partially supported by NSF (Grant DMS-9305742).
Translated fromSibirskii Matematicheskii Zhurnal, Vol. 36, No. 6, pp. 1416–1434, November–December, 1995.
Rights and permissions
About this article
Cite this article
Herron, D.A., Koskela, P. Poincaré domains and quasiconformal mappings. Sib Math J 36, 1232–1246 (1995). https://doi.org/10.1007/BF02106847
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02106847