Riemann surfaces of class $\textrm {A}$
HTML articles powered by AMS MathViewer
- by Robert Osserman
- Trans. Amer. Math. Soc. 82 (1956), 217-245
- DOI: https://doi.org/10.1090/S0002-9947-1956-0094450-1
- PDF | Request permission
References
- Lars Ahlfors, Zur Bestimmung des Typus einer Riemannschen Fläche, Comment. Math. Helv. 3 (1931), no. 1, 173â177 (German). MR 1509432, DOI 10.1007/BF01601810 â, Sur le type dâune surface de Riemann, C. R. Acad. Sci. Paris vol. 201 (1935) pp. 30-32. â, Conformal mapping, Lecture Notes at Oklahoma Agricultural and Mechanical College, Summer, 1951. â, On quasiconformal mappings, Journal dâAnalyse MathĂŠmatique vol. 3 (1953) pp. 1-58. L. Lichtenstein, Beweis des Satzes, dass jedes hinreichend kleine, im wesentlichen stetig gekrĂźmmte, singularitätenfreie FlächenstĂźck auf einer Teil einer Ebene zusammenhängend und in den kleinsten Teilen ähnlich abgebildet werden kann, Abhandlungen der KĂśniglichen Preussichen Akademie der Wissenschaften zu Berlin, Physikalish-Mathematische Classe, 1911, Abh. VI, pp. 1-49.
- Gerald R. MacLane, Concerning the uniformization of certain Riemann surfaces allied to the inverse-cosine and inverse-gamma surfaces, Trans. Amer. Math. Soc. 62 (1947), 99â113. MR 21596, DOI 10.1090/S0002-9947-1947-0021596-0 P. J. Myrberg, Ăber die Bestimmung des Typus einer Riemannschen Fläche, Annales Academiae Scientiarum Fennicae Ser. A vol. 45 No. 3 (1935) pp. 1-30. R. Osserman, On a conjecture in the problem of type for simply-connected Riemann surfaces, Proceedings of the International Mathematical Congress, Amsterdam, Sept. 1954, vol. 2, p. 153.
- Robert Osserman, A hyperbolic surface in $3$-space, Proc. Amer. Math. Soc. 7 (1956), 54â58. MR 76042, DOI 10.1090/S0002-9939-1956-0076042-9
- D. B. PotyagaÄlo, Condition of hyperbolicity of a class of Riemannian surfaces, Ukrain. Mat. Ĺ˝urnal 5 (1953), 459â463 (Russian). MR 0061179 O. TeichmĂźller, Eine Anwendung quasikonformer Abbildungen auf das Typenproblem, Deutsche Mathematik vol. 2 (1937) pp. 321-327.
- L. I. VolkovyskiÄ, The determination of the type of certain classes of simply connected Riemann surfaces, Mat. Sbornik N.S. 23(65) (1948), 229â258 (Russian). MR 0027856
- Hassler Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), no. 1, 63â89. MR 1501735, DOI 10.1090/S0002-9947-1934-1501735-3
Bibliographic Information
- © Copyright 1956 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 82 (1956), 217-245
- MSC: Primary 30.00
- DOI: https://doi.org/10.1090/S0002-9947-1956-0094450-1
- MathSciNet review: 0094450