• 충청수학회지
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• 제20권1호
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• pp.71-80
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• 2007

In this article, we consider axes of a minimal surface in $R^3$ of genus zero with a planar end, and then prove that two consecutive axes near planar end must be parallel but cannot be in a same line.

• 대한수학회지
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• 제48권5호
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• pp.1083-1100
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• 2011

We show that some class of spacelike maximal surfaces and timelike minimal surfaces match smoothly across the singular curve of the surfaces. Singular Bj$\"{o}$rling representation formulae for generalized spacelike maximal surfaces and for generalized timelike minimal surfaces play important roles in the explanation of this phenomenon.

• 호남수학학술지
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• 제44권1호
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• pp.98-109
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• 2022

In the present paper, we prove the growth and distortion theorems for the spirallike functions class 𝓢_k(λ) related to boundary radius rotation, and by using the distortion result, we get an estimate for the Gaussian curvature of a minimal surface lifted by a harmonic function whose analytic part belongs to the class 𝓢_k(λ). Moreover, we determine and draw the minimal surface corresponding to the harmonic Koebe function.

• 충청수학회지
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• 제34권4호
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• pp.379-385
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• 2021

We consider the local uniqueness of a catenoid under the condition for the Gaussian curvature analogous to Bianchi surfaces. More precisely, if a nonplanar minimal surface in ℝ³ has the Gaussian curvature $K={\frac{1}{(U(u)+V(v))^2}}$ for any functions U(u) and V (v) with respect to a line of curvature coordinate system (u, v), then it is part of a catenoid. To do this, we use the relation between a conformal line of curvature coordinate system and a Chebyshev coordinate system.

• 충청수학회지
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• 제19권3호
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• pp.219-224
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• 2006

In this article, we prove that a properly embedded minimal surface in $R^3$ of genus zero must be one of Riemann's minimal examples if outside of a solid cylinder it is the union of planar ends with the same torques at all integer heights.

• Korean Journal of Mathematics
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• 제23권3호
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• pp.439-446
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• 2015

In this paper we consider the meromorphic function G(z) with a pole of order 1 at -a and analytic function F(z) with a zero -a of order 2 in $\mathbb{D}=\{z :{\mid}z{\mid}<1\}$, where -1 < a < 1. From these functions we obtain the regular simply-connected minimal surface $S=\{(u(z),\;{\nu}(z),\;H(z)):z{\in}\mathbb{D}\}$ in $E^3$ and the harmonic function $f=u+i{\nu}$ defined on $\mathbb{D}$, and then we investigate properties of the minimal surface S and the harmonic function f.

• 충청수학회지
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• 제19권4호
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• pp.313-318
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• 2006

In this paper, we study harmonic mappings related to the nonparametric minimal surfaces that lie over the upper halfplane.

• 대한수학회보
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• 제52권2호
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• pp.679-684
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• 2015

In this paper we discuss bounds for the total curvature of nonparametric minimal surfaces by using the properties of planar harmonic mappings.

• Korean Journal of Mathematics
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• 제7권2호
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• pp.285-289
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• 1999

In this paper, we estimate the total curvature of non-parametric minimal surfaces by using the properties of univalent harmonic mappings defined on ${\Delta}=\{z:{\mid}z:{\mid}>1\}$.

• 한국정밀공학회지
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• 제28권7호
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• pp.834-850
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• 2011

In this paper, a novel tissue engineering scaffold design method based on triply periodic minimal surface (TPMS) is proposed. After generating the hexahedral elements for a 3D anatomical shape using the distance field algorithm, the unit cell libraries composed of triply periodic minimal surfaces are mapped into the subdivided hexahedral elements using the shape function widely used in the finite element method. In addition, a heterogeneous implicit solid representation method is introduced to design a 3D (Three-dimensional) bio-mimetic scaffold for tissue engineering from a sequence of computed tomography (CT) medical image data. CT image of a human spine bone is used as the case study for designing a 3D bio-mimetic scaffold model from CT image data.