A CHARACTERIZATION OF AUTOMORPHISMS OF THE UNIT DISC BY THE POINCARE ́ METRIC
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Non-trivial automorphisms of the unit disc in the complex plane can be classified by three classes; elliptic, parabolic and hyperbolic automorphisms. This classification is due to a representation in the pro- jective special linear group of the real field, or in terms of fixed points on the closure of the unit disc. In this paper, we will characterize this classi- fication by the distance function of the Poincar ́e metric on the interior of the unit disc.
Abstract
Non-trivial automorphisms of the unit disc in the complex plane can be classified by three classes; elliptic, parabolic and hyperbolic automorphisms. This classification is due to a representation in the pro- jective special linear group of the real field, or in terms of fixed points on the closure of the unit disc. In this paper, we will characterize this classi- fication by the distance function of the Poincar ́e metric on the interior of the unit disc.
참고문헌 (10)
- L. V. Ahlfors, "An extension of Schwarz’s lemma", Trans. Amer. Math. Soc, 43, pp.359~364 (1938)
- K.-T. Kim, "Schwarz’s lemma from a differential geometric viewpoint" (2011), IISc Press, World Scientific Publishing Co. Pte. Ltd
- V. V. Kisil, "Geometry of M¨obius transformations" (2012), Imperial College Press
- S. Kobayashi, "Hyperbolic manifolds and holomorphic mappings" (1970), Marcel Dekker, Inc
- S. Kobayashi, (1998), Springer-Verlag
- P. Koebe, "Nachr. Ges. Wiss. G¨ottingen, Math.-Phys. Kl., 1907", pp.177~190 (1907)
- S. Lang, "SL2(R)" (1975), Addison-Wesley Publishing Co.
- K. -H. Lee, "On parabolic and hyperbolic automorphisms of the unit disc", Internat. J. Math. Anal, 9, pp.1405~1413 (2015)
- 이강혁, "An Intrinsic Criterion for the Type of Automorphisms of the Unit Disc", East Asian Mathematical Journal, 37(3), pp.307~317 (2021), 영남수학회
- H. Poincar´e, "Sur l’uniformisation des fonctions analytiques", Acta Math., 31, pp.1~63 (1908)