Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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AFFINE HOMOGENEOUS DOMAINS IN THE COMPLEX PLANE

  • Kang-Hyurk, Lee (Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University)
  • Received : 2022.11.11
  • Accepted : 2022.11.29
  • Published : 2022.12.30
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Abstract

In this paper, we will describe affine homogeneous domains in the complex plane. For this study, we deal with the Lie algebra of infinitesimal affine transformations, a structure of the hyperbolic metric involved with affine automorphisms. As a consequence, an affine homogeneous domain is affine equivalent to the complex plane, the punctured plane or the half plane.

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Acknowledgement

This work was supported by Samsung Science and Technology Foundation under Project Number SSTF-BA2201-01.

References

  1. L. V. Ahlfors. An extension of Schwarz's lemma, Trans. Amer. Math. Soc. 43 (1938) 359-364.  https://doi.org/10.1090/S0002-9947-1938-1501949-6
  2. L. V. Ahlfors. Complex analysis. International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., New York, third edition, 1978. An introduction to the theory of analytic functions of one complex variable. 
  3. Y.-J. Choi and K.-H. Lee. Existence of a complete holomorphic vector field via the Kahler-Einstein metric, Ann. Global Anal. Geom. 60 (2021) 97-109.  https://doi.org/10.1007/s10455-021-09769-2
  4. Y.-J. Choi, K.-H. Lee, and S. Yoo. A certain Kahler potential of the Poincar'e metric and its characterization, J. Korean Math. Soc. 57 (2020) 1335-1345.  https://doi.org/10.4134/JKMS.J190640
  5. C. Kai and T. Ohsawa. A note on the Bergman metric of bounded homogeneous domains, Nagoya Math. J. 186 (2007) 157-163.  https://doi.org/10.1017/S0027763000009399
  6. P. Koebe. Uber die Uniformisierung reeller algebraischer Kurven. Gott. Nachr. 1907 (1907) 177-190. 
  7. K.-H. Lee. A method of potential scaling in the study of pseudoconvex domains with noncompact automorphism group, J. Math. Anal. Appl. 499 (2021) Paper No. 124997, 15. 
  8. H. Poincare. Sur l'uniformisation des fonctions analytiques, Acta Math. 31 (1908) 1-63. https://doi.org/10.1007/BF02415442