• Journal for History of Mathematics
• /
• v.30 no.1
• /
• pp.1-15
• /
• 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 Chungcheong Mathematical Society
• /
• v.9 no.1
• /
• pp.101-106
• /
• 1996

In this paper, we will consider the Denjoy-Riemann integral of functions mapping a closed interval into a Banach space. We will show that a Riemann integrable function on [a, b] is Denjoy-Riemann integrable on [a, b] and that a Denjoy-Riemann integrable function on [a, b] is Denjoy-McShane integrable on [a, b].

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

• International Journal of CAD/CAM
• /
• v.9 no.1
• /
• pp.103-109
• /
• 2010

Recently, various conformal geometric methods have been presented for non-rigid surface matching and registration. This work proposes to improve the robustness of conformal geometric methods to the boundaries by incorporating the symmetric information of the input surface. We presented two symmetric conformal mapping methods, which are based on solving Riemann-Cauchy equation and curvature flow respectively. Experimental results on geometric data acquired from real life demonstrate that the symmetric conformal mapping is insensitive to the boundary occlusions. The method outperforms all the others in terms of robustness. The method has the potential to be generalized to high genus surfaces using hyperbolic curvature flow.

• East Asian mathematical journal
• /
• v.12 no.2
• /
• pp.203-211
• /
• 1996

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

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

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

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.1
• /
• pp.61-78
• /
• 1995

In this study the method of analysis for three-dimensional plane crack problem by fractional linear mapping is given. Using this method we can obtain the exact solutions of significantly different configurations of the crack. In the example image crack configurations by mapping of elliptic crack are illustrated. And the stress intensity factors along the image crack tips are calculated.

• Journal of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.91-102
• /
• 2002

Let M and N be CR manifolds with nondegenerate Levi forms of hypersurface type of dimension 2m ＋ 1 and 2n ＋ 1, respectively, where 1 $\leq$ m $\leq$ n. Let f : M longrightarrow N be a CR mapping. Under a generic assumption we construct a complete system of finite order for the infinitesimal deformations of f. In particular, we prove the space of infinitesimal deformations of f forms a finite dimensional Lie algebra.