• Journal of the Korean Mathematical Society
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• v.61 no.4
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• pp.761-778
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• 2024

A separable minimal surface is represented by the form of f(x) + g(y) + h(z) = 0, where f, g and h are real-valued functions of x, y and z, respectively. We provide exact equations for separable minimal surfaces with elliptic functions that are singly, doubly and triply periodic minimal surfaces and completely classify all them. In particular, parameters in the separable minimal surfaces change the shape of the surfaces, such as fundamental periods and its limit behavior, within the form f(x) + g(y) + h(z) = 0.

• Journal of the Korean housing association
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• v.15 no.6
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• pp.15-25
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• 2004

This study examined how the characteristics of abstractive form among various contenporary housing architecture have been expressed. The conclusions were: First, abstractive characteristics and types related to from expression of contemporary housing architectures were minimal form and absolute form of geometrical abstraction, plastic form and atypical form of expressive abstraction and mechanical aesthetics of industrial abstraction. Second, the typological form expression characteristics in minimal expression related to geometrical abstraction were simplicity, purity, and the properties of matter, and the characteristics in absolute expression were overlapping, obliqueness and dispensability. On the other hand, plasticity and mobility of materials were distinctive in plastic form expression, and inclination, curve and asymmetry were distinctive in atypical expression. The distinctive nature of mechanical aesthetics related to industrial abstraction included transparency, simplicity and. the properties of matter Funhermore, the study aimed at the understanding of various from expressions showed up in contemporary housing architecture, revealing the aspects of abstractive form expression characteristics.

• Korean Institute of Interior Design Journal
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• no.25
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• pp.169-175
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• 2000

Since the late 19th Century, modern architecture of definite figure and form shared similar concepts on space and from with the abstract art, pursuing the geometric purity and the abstraction. So the reductive approach had been taken in modern architecture as well as on modern art. The 1960 minimal art had experimented an extreme reduction with the cubic forms and the plane canvases, embodying so called minimal-art content, it was just another version of modernism art interpreted by the extreme reduction. The reduction is a characteristics of modernism adopted in every art field, including architecture. Not from the apparent, but from the essential quality of architectural form, figure and space resulting from the reductive approach, a building in this trend schould be judged and appreciated. In many aspects, Korean traditional architecture has been shown the characteristics of Minimal Architecture. With these points of view, this study analyzes characteristics of Korean traditional architecture with above contents through the form and space.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.143-153
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• 2002

Null designs form a vector space and there are only finite number of minimal null designs(up to scalar multiple), hence it is natural to look at the convex polytopes of minimal null designs. For example, when t = 0, k = 1, the convex polytope of minimal null designs is the polytope of roofs of type An. In this article, we look at the convex polytopes of minimal null designs and find many general properties on the vertices, edges, dimension, and some structural properties that might help to understand the structure of polytopes for big n, t through the structure of smaller n, t.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1201-1207
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• 2013

Let N be a complete Riemannian manifold with nonnegative Ricci curvature and let M be a complete noncompact oriented stable minimal hypersurface in N. We prove that if M has at least two ends and ${\int}_M{\mid}A{\mid}^2\;dv={\infty}$, then M admits a nonconstant harmonic function with finite Dirichlet integral, where A is the second fundamental form of M. We also show that the space of $L^2$ harmonic 1-forms on such a stable minimal hypersurface is not trivial. Our result is a generalization of one of main results in [12] because if N has nonnegative sectional curvature, then M admits no nonconstant harmonic functions with finite Dirichlet integral. And our result recovers a main theorem in [3] as a corollary.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.649-668
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• 2000

In this paper we prove the following : Let M be a real (2n-1)-dimensional compact minimal semi-invariant submanifold in a complex projective space P(sub)n+1C. If the scalar curvature $\geq$2(n-1)(2n+1), then m is a homogeneous type $A_1$ or $A_2$. Next suppose that the third fundamental form n satisfies dn = 2$\theta\omega$ for a certain scalar $\theta$$\neq$c/2 and $\theta$$\neq$c/4 (4n-1)/(2n-1), where $\omega$(X,Y) = g(X,øY) for any vectors X and Y on a semi-invariant submanifold of codimension 3 in a complex space form M(sub)n+1 (c). Then we prove that M has constant principal curvatures corresponding the shape operator in the direction of the distingusihed normal and the structure vector ξ is an eigenvector of A if and only if M is locally congruent to a homogeneous minimal real hypersurface of M(sub)n (c).

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.421-426
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• 2008

Let $M^n$ be a complete immersed super stable minimal submanifold in $\mathbb{R}^{n+p}$ with fiat normal bundle. We prove that if M has finite total $L^2$ norm of its second fundamental form, then M is an affine n-plane. We also prove that any complete immersed super stable minimal submanifold with flat normal bundle has only one end.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.253-266
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• 2011

In this paper we give an upper bound of the first eigenvalue of the Laplace operator on a complete stable minimal hypersurface M in the hyperbolic space which has finite $L^2$-norm of the second fundamental form on M. We provide some sufficient conditions for minimal hypersurface of the hyperbolic space to be stable. We also describe stability of catenoids and helicoids in the hyperbolic space. In particular, it is shown that there exists a family of stable higher-dimensional catenoids in the hyperbolic space.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.327-335
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• 2005

For a compact and orientable minimal real hypersurface $M\;in\;QP^n$, we prove that if the minimum of the sectional curvatures of Mis 3/(4n - 1), then M is isometric to the geodesic minimal hypersphere $M_{0,n-1}^Q$.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.1
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• pp.426-435
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• 2013

Minimal architecture is generally expressed in a simple and pure form, this characteristic of minimal architecture was first introduced by the architect, Mies Van der Roche, in the beginning of 20th century. The objective of this study is to identify wether minimal architecture is just a reappearance of the beginning of 20th century's modern architecture or a suitable form for contemporary aesthetics. As a result, it can be concluded that minimal architecture is based on human emotion and one's experienced perception which is very different from the modern architecture which is more focused on functionality and mechanical esthetics. Minimal architecture uses two systems which are multi-sensual perception and conceptual perception; however, it focuses more on conceptual perception which is also used in comtemporary architecture. In conclusion, simplicity is just one of the necessary conditions which is not sufficient enough to represent minimal architecture.