Seongdeog Yang

We construct embedded closed minimal surfaces in the round three-sphere ${\Bbb S}^3(1)$, resembling two parallel copies of the Clifford torus, joined by $m^2$ small catenoidal bridges symmetrically arranged along a square lattice of points on the torus.

Space-like maximal surfaces and time-like minimal surfaces in\nLorentz-Minkowski3-space are both characterized as zero mean curvature\nsurfaces. We are interested in the case where the zero mean curvature surface\nchanges type from space-like to time-like at a given non-degenerate null curve.\nWe consider this phenomenon and its interesting connection to 2-dimensional\nfluid mechanics in this expository article.\n

It is well known that space-like maximal surfaces and time-like minimal surfaces in Lorentz–Minkowski 3-space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="bold">L</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:math> have singularities (i.e. points where the induced metric degenerates) in general. We are interested in the case where the singular set consists of a light-like line, since this

We prove the existence of an infinite family of complete spacelike maximal surfaces with singularities in Lorentz-Minkowski three-space and study their properties. These surfaces are distinguished by their number of handles and have two elliptic catenoidal ends.

It is well-known that space-like maximal surfaces and time-like minimal surfaces in Lorentz--Minkowski $3$-space $\boldsymbol{R}^{3}_{1}$ have singularities in general. They are both characterized as zero mean curvature surfaces. We are interested in the case where the singular set consists of a light-like line, since this case has not been analyzed before. As a continuation of a previous work by the authors, we give the first example of a family of such surfaces which change type across a light

We construct embedded triply periodic zero mean curvature surfaces of mixed type in the Lorentz-Minkowski 3-space with the same topology as the Schwarz D surface in the Euclidean 3-space.

We show that some class of spacelike maximal surfaces and timelike minimal surfaces match smoothly across the singular curve of the surfaces. Singular Bjorling representation formulae for generalized spacelike maximal surfaces and for generalized timelike minimal surfaces play important roles in the explanation of this phenomenon.

The first author studied spacelike constant mean curvature one (CMC-1) surfaces in the de Sitter 3-space S 3 1 when the surfaces have no singularities except within some compact subsets and are of finite total curvature on the complement of this compact subset. However, there are many CMC-1 surfaces whose singular sets are not compact. In fact, such examples have already appeared in the construction of trinoids given by Lee and the last author via hypergeometric functions.

국내 택배시장은 과거 몇 개의 업체에서 독점해왔으나 현재는 대기업들과 수많은 중소기업들이 참여하고 있어 경쟁이 심화되고 있다. 우편물의 신속한 배송과 운송비용의 최소화는 매우 중요하며 이를 위하여 운송거리의 최단거리화가 우선 필요하다. 본 논문은 전국의 주요 도시에 배치된 우편집중국을 기하적으로 가장 짧게 연결하는 교환센터의 최적 위치를 찾는 방법을 제시한다. 송전계통의 routing, 배전선로망의 최적화 등에 이용되고 있는 Steiner Tree 이론을 최단거리 우편물 운송망 구축에 적용하였다. Steiner Tree 이론으로부터 선정된 위치에 교환센터를 설치할 경우, 운송비를 절감하여 경영수지를 개선할 뿐 아니라 신속한 배달을 최우선으로 하는 택배 시장에서 우위를 점할 수 있을 것으로 기대된다. Steiner Tree 이론은 차기 초고압 선로를 최단거리로 연결하는 전력소의 위치선정 등에도 활용될 수 있을 것으로 사료된다.

We solve the Börling problem for constant mean curvature one surfaces in hyperbolic three-space and in de Sitter three-space. That is, we show that for any regular, analytic (and spacelike in the case of de Sitter three-space) curve γ and an analytic (timelike in the case of de Sitter three-space) unit vector field $N$ along and orthogonal to γ, there exists a unique (spacelike in the case of de Sitter three-space) surface of constant mean curvature 1 which contains γ and the unit normal of whic