• Journal for History of Mathematics
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• v.30 no.1
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• pp.1-15
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• 2017

The original proof-argument of Riemann in 1851 for the Riemann mapping theorem, one of the most central theorems in Complex analysis, was found faulty and essentially buried underneath the proof by $Carath{\acute{e}}odory$ of 1929, now accepted as the "textbook" proof. On the other hand, the original Riemann's "proof" was rediscovered and made correct by R.E. Greene and the author of this article in 2016. In this article, we try to shed lights onto the history related to the Riemann mapping theorem and the surrounding developments of 1850-1930 by reflecting upon the main flow of ideas and methods of the proof by R. E. Greene and K.-T. Kim.

• Journal of the Korean Mathematical Society
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• v.37 no.2
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• pp.285-295
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• 2000

It is well-known that there is no analogue to the Riemann mapping theorem in the higher dimensional case. Therefore, it would be an interesting question to find sufficient conditionsl for domains to be biholomorphically equivalent to the unit bal. In this paper, we investigate this questionin the case where the given domains are generalized complex ellipsoids with spherical boundary points.

• Kyungpook Mathematical Journal
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• v.8 no.2
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• pp.47-48
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• 1968

• Kyungpook Mathematical Journal
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• v.8 no.2
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• pp.49-50
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• 1968

• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.115-123
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• 1994

The Bergman kernel is closely connected to mapping problems in complex analysis. For example, the Riemann mapping function is witten down in terms of the Bergman kernel. Hence, information about the bergman kernel gives information about mappings. In this note, we prove the following theorem.