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A Note on the Uniqueness of Koebe–Andreev–Thurston Theorem

A Note on the Uniqueness of Koebe–Andreev–Thurston Theorem
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摘要 In this paper, we present a new proof of the uniqueness of Koebe-Andreev-Thurston theorem. Our method is based on the argument principle in complex analysis and reviews the connection between the circle packing theorem and complex analysis. In this paper, we present a new proof of the uniqueness of Koebe-Andreev-Thurston theorem. Our method is based on the argument principle in complex analysis and reviews the connection between the circle packing theorem and complex analysis.
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第7期1469-1474,共6页 数学学报(英文版)
基金 Supported by National Natural Science Foundation of China (Grant No. 10701084)
关键词 Circle packing argument principle MSbius transformation Circle packing, argument principle, MSbius transformation
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参考文献5

  • 1Koebe, P.: Kontaktktprobleme der konformen Abbildung. Bet. Siichs. Akad. Wiss. Leizig, Math.-Phys. Kl., 88, 141-164 (1936).
  • 2Thurston, W.: The geometry and topology of 3-manifolds. Princeton University Notes, Princeton, New Jersey, 1982.
  • 3Marden, A., Rodin, B.: On Thurston's formulation and proof of Andreev's theorem. Lecture Notes in Mathematics, 1435, Springer, 1989, 103-164.
  • 4He, Z. X., Schramm, O.: Fixed points, Koebe uniformization and circle packings. Ann. of Math., 137, 369-406 (1993).
  • 5Lee, J. M.: Introduction to Smooth Manifolds, Springer, New York, 2003.

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