Abstract
We investigate the modulus problem for families of curves in multiply-connected nonorientable domains on a Riemannian Mobius strip. We determine the extremal metric and the modulus of a “cross” family of arcs.
Similar content being viewed by others
References
P. M. Tamrazov, Method of Extremal Metrics and Conformal Mappings [in Russian], Candidate-Degree Thesis (Physics and Mathematics), Kiev (1963).
P. M. Tamrazov, “On some extremal problems in the theory of conformal mappings,” Mat. Sb., 109, No. 3. 329–337 (1965).
P. M. Tamrazov, “Conformally invariant moduli and circular symmetrization.” in: Metric Problems in the Theory of Functions and Mappings [in Russian], Naukova Dumka. Kiev (1974), pp. 127–146.
P. M. Tamrazov, “Methods for investigation of extremal metrics and moduli of families of curves on a twisted Riemannian manifold,” Mat. St., 183, No. 3, 55–75 (1992).
P. M. Tamrazov, “Moduli and extremal metrics on nonorientable and twisted Riemannian manifolds,” Ukr. Mat. Zh., 50, No. 10. 1388–1398 (1998).
P. M. Tamrazov, “Moduli and extremal metrics on twisted Riemannian manifolds,” in: Moduli of Nonorientable and Twisted Riemannian Manifolds [in Russian], Preprint No. 9, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1997), pp. 1–25.
J.A. Jenkins, Univalent Functions and Conformal Mapping, Springer, Berlin 1958.
H. Grotzsch, “Das Kreissbogenschlitztheorem der konformen Abbildung mehrfach zusammenhangender schlichter Bereiche. I,” Leipzig. Ber., 83, No. 4, 238–253 (1931).
P. M. Tamrazov and S. A. Okhrimenko, “Pairwise products of moduli of families of curves on a Riemannian Mobius strip,” Ukr. Mat. Zh., 51, No. 1, 110–116 (1999).
S. A. Okhrimenko and P. M. Tamrazov, “Estimates of products of moduli of families of curves on a Riemannian Mobius strip,” in: Moduli of Nonorientable and Twisted Riemannian Manifolds [in Russian], Preprint No. 9, Institute of Mathematics. Ukrainian Academy of Sciences, Kiev (1997), pp. 26–40.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Okhrimenko, S.A. Moduli of multiply-connected domains on a Riemannian Mobius strip. Ukr Math J 52, 407–412 (2000). https://doi.org/10.1007/BF02513135
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02513135