This is a preview of subscription content, log in via an institution to check access.
References
G. D. Mostow, “Quasi-conformal mappings inn-space and the rigidity of hyperbolic space forms,” Inst. Hautes études Sci. Publ. Math., No. 34, 53–104 (1968).
D. E. Menchoff, “Sur une generalization d'un theoreme de M. H. Bohr,” Mat. Sb.,2, No. 44, 339–356 (1937).
Yu. G. Reshetnyak, Space Mappings with Bounded Distortion [in Russian], Nauka, Novosibirsk (1982).
J. VÄisÄlÄ, Lectures onn-Dimensional Quasiconformal Mappings, Springer, Berlin etc. (1971). (Lecture Notes in Math.;229.)
B. Fuglede, “Extremal length and functional completion,” Acta Math., No. 98, 171–219 (1957).
P. Pansu, “Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un,” Ann. of Math.,129, 1–60 (1989).
G. D. Mostow, Strong Rigidity of Locally Symmetric Spaces, Tokyo Univ. Press, Princeton (1973).
G. D. Mostow, “A remark on quasiconformal mappings on Carnot groups,” Mich. Math. J.,41, No. 1, 31–38 (1994).
A. Koranyi and H. M. Reimann, “Foundations for the theory of quasiconformal mappings on the Heisenberg group,” Adv. in Math.,111, 1–87 (1995).
G. B. Folland and E. M. Stein, “Hardy spaces on homogeneous groups,” Math. Notes,28, Princeton Univ. Press, Princeton (1982).
S. K. Vodop'yanov, “Function spaces and quasiconformal mappings on homogeneous groups,” in: Proceedings of the 5th Republican Conference on Nonlinear Problems of Mathematical Physics (L'vov, September 9–17, 1985) [in Russian], Donetskii Univ., Kiev, 1987, pp. 107–109; submitted to UkrNIINTI on Jule 16, 1987, No. 2077.
S. K. Vodop'yanov, “L p -potential theory and quasiconformal mappings on homogeneous groups,” in: Contemporary Problems of Geometry and Analysis [in Russian], Trudy Inst. Mat. Vol. 14 (Novosibirsk), Nauka, Novosibirsk, 1989, pp. 45–89.
S. K. Vodop'yanov, “Quasiconformal mappings on Carnot groups,” in: Abstracts: The International Conference on Algebra and Analysis (Kazan', June, 1994), Kazan', 1994, pp. 33–34.
H. Federer, Geometric Measure Theory [Russian translation], Nauka, Moscow (1987).
G. E. Shilov and B. L. Gurevich, Integral, Measure, and Derivative [in Russian], Nauka, Moscow (1964).
O. Martio, S. Rickman, and J. VÄisÄlÄ, “Definitions for quasiregular mappings,” Ann. Acad. Sci. Fenn. Ser. A I Math., No. 448, 1–40 (1969).
A. Koranyi and S. Vagi, “Singular integrals in homogeneous spaces and some problems of classical analysis,” Ann. Scuola Norm. Sup. Pisa. Cl. Sci. (4),25, 575–648 (1971).
S. K. Vodop'yanov and A. D. Ukhlov, “Weakly contact transformations and change of variables in nilpotent groups,” Dokl. RAN,341, No. 4, 439–441 (1995).
S. K. Vodop'yanov, “Analysis on Carnot groups and quasiconformal mappings,” in: Abstracts: Ann Arbor Analysis Workshop (Ann Arbor, August, 1995), University of Michigan, Ann Arbor, 1995, pp. 5–6.
Author information
Authors and Affiliations
Additional information
The research was supported by the Russian Foundation for Fundamental Research (Grant 94-01-00378) and the International Science Foundation (Grant RAT000).
Translated fromSibirskii Matematicheskii Zhurnal, Vol. 36, No. 6, pp. 1317–1327, November–December, 1995.
Rights and permissions
About this article
Cite this article
Vodop'yanov, S.K., Greshnov, A.V. Analytic properties of quasiconformal mappings on Carnot groups. Sib Math J 36, 1142–1151 (1995). https://doi.org/10.1007/BF02106836
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02106836