• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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• pp.147-156
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• 2007

We introduce the extremal length and examine its properties. And we consider the geometric applications of extremal length to the boundary behavior of analytic functions, conformal mappings. We derive the theorem in connection with the capacity. This theorem applies the extremal length to the analytic function defined on the domain with a number of holes. And we obtain the theorems in connection with the pure geometric problems.

• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.39-50
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• 2014

In this paper, we study screen quasi-conformal irrotational half lightlike submanifolds M of a semi-Riemannian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection, whose structure vector field ${\zeta}$ is tangent to M. The main result is a classification theorem for such Einstein half lightlike submanifolds of a Lorentzian space form admitting a semi-symmetric non-metric connection.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.101-108
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• 1997

We let (M,g) be a noncompact complete Riemannina manifold of dimension $n \geq 3$ with finite volume and positive scalar curvature. We show the existence of a conformal metric with constant positive scalar curvature on (M,g) by gluing solutions of Yamabe equation on each compact subsets $K_i$ with $\cup K_i = M$ .

• Radiation Oncology Journal
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• v.36 no.1
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• pp.1-10
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• 2018

Intensity-modulated radiation therapy (IMRT) has been considered the most successful development in radiation oncology since the introduction of computed tomography into treatment planning that enabled three-dimensional conformal radiotherapy in 1980s. More than three decades have passed since the concept of inverse planning was first introduced in 1982, and IMRT has become the most important and common modality in radiation therapy. This review will present developments in inverse IMRT treatment planning and IMRT delivery using multileaf collimators, along with the associated key concepts. Other relevant issues and future perspectives are also presented.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.347-354
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• 1997

The conharmonic transforamtion is a conformal transformation which satisfies a specified differential equation. Such a transformation was defined by Y. Ishi and we generalize his results. In particular, we obtain a necessary and sufficient condition for the invariance of critical Riemannian metrics under the conharmonic transformation.

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.195-201
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• 1998

We let (M,g) be a noncompact complete Riemannian manifold of dimension n $\geq$ 3 with scalar curvatue S, which is close to -1. We show the existence of a conformal metric $\bar{g}$, near to g, whose scalar curvature $\bar{S}$ = -1 by gluing solutions of the corresponding partial differential equation on each bounded subsets $K_i$ with ${\bigcup}K_i$ = M.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.365-377
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• 2016

In this paper, we study half lightlike submanifolds M of an indefinite Kaehler manifold $\bar{M}$ of quasi-constant curvature such that the characteristic vector field ${\zeta}$ of $\bar{M}$ is tangent to M. First, we provide a new result for such a half lightlike submanifold. Next, we investigate a statical half lightlike submanifold M of $\bar{M}$ subject such that (1) the screen distribution S(TM) is totally umbilical or (2) M is screen conformal.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1367-1376
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• 2013

We study Einstein lightlike hypersurfaces M of a Lorentzian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection subject to the conditions; (1) M is screen conformal and (2) the structure vector field ${\zeta}$ of $\tilde{M}$ belongs to the screen distribution S(TM). The main result is a characterization theorem for such a lightlike hypersurface.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.223-230
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• 2001

In this parper, we considered the uniqueness of positive time-solution to equation ${\Box}_g$u(t,$\chi$) - $c_n$u(t,$\chi$) + $c_n$u(t,$\chi$)$^[\frac{n+3}{n-3}]$ = 0, where $c_n$ = $\frac{n-1}{4n}$ and ${\Box}_g$ is the d'Alembertian for a Lorentzian warped manifold M = {a,$\infty$] $\times_f$ N.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.225-234
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• 2010

In this paper, we study the geometry of lightlike hypersurfaces of a semi-Riemannian manifold. We prove a classification theorem for Einstein lightlike hypersurfaces M of a Lorentzian space form subject such that the second fundamental forms of M and its screen distribution S(TM) are conformally related by some non-vanishing smooth function.