• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.471-479
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• 2015

In this paper, we prove that any stable f-harmonic map ${\psi}$ from ${\mathbb{S}}^2$ to N is a holomorphic or anti-holomorphic map, where N is a $K{\ddot{a}}hlerian$ manifold with non-positive holomorphic bisectional curvature and f is a smooth positive function on the sphere ${\mathbb{S}}^2$with Hess $f{\leq}0$. We also prove that any stable f-harmonic map ${\psi}$ from sphere ${\mathbb{S}}^n$ (n > 2) to Riemannian manifold N is constant.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1337-1346
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• 2015

We examine the relationship of the shape operator of a surface of Euclidean 3-space with its Gauss map of pointwise 1-type. Surfaces with constant mean curvature and right circular cones with respect to some properties of the shape operator are characterized when their Gauss map is of pointwise 1-type.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.553-574
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• 2018

In this paper, we study harmonic maps and biharmonic maps on the principal G-bundle in Kobayashi and Nomizu and also the warped product $P=M{\times}_fF$ for a $C^{\infty}$(M) function f on M studied by Bishop and O'Neill, and Ejiri.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.3
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• pp.259-264
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• 2012

Automatic magnetic abrasive polishing (MAP), which can be applied after machining of a mold on a machine tool without unloading, is very effective for finishing a free-form surface such as a complicated injection mold. This study aimed to improve the efficiency of MAP of a non-ferrous mold surface. The magnetic array table and control of the electromagnet polarity were applied in the MAP of a free-form surface. In this study, first, the magnetic flux density on the mold surface was simulated to determine the optimal conditions for the polarity array. Then, the MAP efficiency for polishing a non-ferrous mold surface was estimated in terms of the change in the radius of curvature and the magnetic flux density. The most improved surface roughness was observed not only in the upward tool path but also in the working area of larger magnetic flux density.

• The KIPS Transactions:PartA
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• v.11A no.5
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• pp.391-400
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• 2004

Within multimodal medical image registration techniques, which correlate different images and Provide integrated information, surface registration methods generally minimize the surface distance between two modalities. However, the features of two modalities acquired from one subject are similar. So, it can improve the accuracy of registration result to match two images based on optimization of both surface distance and shape feature. This research proposes a registration method which optimizes surface distance and surface curvature of two brain modalities. The registration process has two steps. First, surface information is extracted from the reference images and the test images. Next, the optimization process is performed. In the former step, the surface boundaries of regions of interest are extracted from the two modalities. And for the boundary of reference volume image, distance map and curvature map are generated. In the optimization step, a transformation minimizing both surface distance and surface curvature difference is determined by a cost function referring to the distance map and curvature map. The applying of the result transformation makes test volume be registered to reference volume. The suggested cost function makes possible a more robust and accurate registration result than that of the cost function using the surface distance only. Also, this research provides an efficient means for image analysis through volume visualization of the registration result.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.859-881
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• 2010

The helicoidal surface is a generalization of rotation surface in a Minkowski space. We study helicoidal surfaces in a Minkowski 3-space in terms of their Gauss map and provide some examples of new classes of helicoidal surfaces with constant mean curvature in a Minkowski 3-space.

• The Pure and Applied Mathematics
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• v.9 no.2
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• pp.107-111
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• 2002

In this article, we prove various properties and some Liouville type theorems for quasi-strongly p-harmonic maps. We also describe conditions that quasi-strongly p-harmonic maps become p-harmonic maps. We prove that if $\phi$ : $M\;\longrightarrow\;N$ is a quasi-strongly p-harmonic map (\rho\; $\geq\;2$) from a complete noncompact Riemannian manifold M of nonnegative Ricci curvature into a Riemannian manifold N of non-positive sectional curvature such that the $(2\rho－2)$-energy, $E_{2p-2}(\phi)$ is finite, then $\phi$ is constant.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.97-103
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• 2013

As a suitable application of the well known generalized maximum principle of Omori-Yau, we obtain rigidity results concerning to a complete hypersurface immersed with bounded mean curvature in the $(n+1)$-dimensional hyperbolic space $\mathbb{H}^{n+1}$. In our approach, we explore the existence of a natural duality between $\mathbb{H}^{n+1}$ and the half $\mathcal{H}^{n+1}$ of the de Sitter space $\mathbb{S}_1^{n+1}$, which models the so-called steady state space.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.447-455
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• 2005

In this article, we introduce the notion of pointwise 1-type Gauss map of the first and second kinds and study surfaces of revolution with such Gauss map. Our main results state that surfaces of revolution with pointwise 1-type Gauss map of the first kind coincide with surfaces of revolution with constant mean curvature; and the right cones are the only rational surfaces of revolution with pointwise 1-type Gauss map of the second kind.

• Journal of the Optical Society of Korea
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• v.15 no.1
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• pp.68-73
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• 2011

This study investigated, using the Orbscan II topography system, the influence of age and sex related changes on the corneal thickness and anterior corneal curvature, more specifically the fine structure of the cornea, in a Korean young population. The Orbscan II topography system is a computer-assisted slit-beam scanning technology that can map the anterior section of the cornea. The mean central corneal thickness of all subjects was $547.532{\pm}44.529\;{\mu}m$. There was no statistical difference (p>0.5) in the mean central corneal thickness between males and females. Sex and age related changes in the mean central corneal thickness had no specific statistical difference (P>0.5). There was a negative correlation between the anterior corneal curvature and the central corneal thickness in all subjects, except for the twenty year olds. However, the thickness relationship between the mean central corneal and the eight paracentral corneal thicknesses had strong statistical differences in all subjects. Also age and sex related changes in the central corneal thickness and the anterior corneal curvature in all subjects had no statistically significant difference, except from 20-26 years old (p>0.05). This information could be a suitable reference basis for future studies in the young population of Asia and for the development of examination tools for corneal refractive surgery.