• 대한수학회지
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• 제61권4호
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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.

• 한국주거학회논문집
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• 제15권6호
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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.

• 한국실내디자인학회논문집
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• 제25호
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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.

• 대한수학회논문집
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• 제17권1호
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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.

• 대한수학회보
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• 제50권4호
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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.

• 대한수학회논문집
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• 제15권4호
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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).

• 대한수학회논문집
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• 제23권3호
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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.

• 대한수학회지
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• 제48권2호
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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.

• 대한수학회보
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• 제42권2호
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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 $M_{0,n-1}^Q$.

• 한국산학기술학회논문지
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• 제14권1호
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• pp.426-435
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• 2013

미니멀 건축의 단순성으로 인하여 최초 시도자를 흔히 20세기 초기 건축가 미스 반 데 로에(Mies van der Rohe)로 잡고 있다. 그렇다면 미니멀 건축이 20세기 초의 근대미학으로 되돌아가는 회귀성 건축인지 그리고 어떻게 이러한 건축이 20세기 후반의 대표적 건축양식 중 하나로 자리 잡고 있는지 알아보고자 하였다. 그 결과, 미니멀 건축은 기능성, 합리성, 위생성 등을 추구하며 장식을 배제하고 단순한 형태의 기계미학을 표현한 근대건축과는 달리 인간의 감성과 체험된 지각에 중점에 두고 간결하고 단순한 형태를 주변공간과 일체화시켜 새로운 질서를 구축하여 감동을 주려고 노력하였음을 알 수 있었다. 이러한 미니멀 건축의 표현 방법은 다감각적 지각 체계와 추상적이며 순수한 개념적 지각 체계 중 개념적 지각체계를 보다 강조하며 대비하여 나타내고 있는 현대건축표현 경향과 일맥상통하고 있다는 것을 알 수 있었다. 그러므로 단순성의 표현만으로는 미니멀 건축을 위한 필요조건은 되지만 충분조건은 되지 않는 것을 알 수 있었다.