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Embedding of the Teichm\"uller space into the Goldman space
김홍찬 대한수학회 2006 대한수학회지 Vol.43 No.6
In this paper we shall explicitly calculate the formulaof the algebraic presentation of an embedding of the Teichmullerspace T(M ) into the Goldman space G(M ). From this algebraicpresentation, we shall show that the Goldman's length parameteron G(M ) is an isometric extension of the Fenchel-Nielsen's lengthparameter onT(M ):
INVOLUTIONS AND THE FRICKE SPACES OF SURFACES WITH BOUNDARY
김홍찬 대한수학회 2014 대한수학회지 Vol.51 No.2
The purpose of this paper is to find expressions of the Fricke spaces of some basic surfaces which are a three-holed sphere Σ(0,3), a one-holed torus Σ(1,1), and a four-holed sphere Σ(0,4). For this goal, we define the involutions corresponding to oriented axes of loxodromic elements and an inner product < , > which gives the information about locations of axes of loxodromic elements. The signs of traces of holonomy elements, which are calculated by lifting a representation from PSL(2,C) to SL(2,C), play a very important role in determining the discreteness of holonomy groups.
김홍찬,연규봉,김원종,박철순 한국전자통신연구원 2019 ETRI Journal Vol.41 No.6
We proposed a novel electromagnetic band‐gap (EBG) cell‐embedded antenna structure for reducing the interference that radiates at the antenna edge in wireless access in vehicular environment (WAVE) communication systems for vehicle‐to‐everything communications. To suppress the radiation of surface waves from the ground plane and vehicle, EBG cells were inserted between micropatch arrays. A simulation was also performed to determine the optimum EBG cell structure located above the ground plane in a conformal linear microstrip patch array antenna. The characteristics such as return loss, peak gain, and radiation patterns obtained using the fabricated EBG cell‐embedded antenna were superior to those obtained without the EBG cells. A return loss of 35.14 dB, peak gain of 10.15 dBi at 80°, and improvement of 2.037 dB max at the field of view in the radiation beam patterns were obtained using the proposed WAVE antenna.
Discrete conditions for the holonomy group of a pair of pants
김홍찬 대한수학회 2007 대한수학회지 Vol.44 No.3
A pair of pants Sigma(0,3) is a building block of orientedsurfaces. The purpose of this paper is to determine thediscrete conditions for the holonomy group piof hyperbolic structure of a pair of pants.For this goal, we classify the relationsbetween the locations of principal lines and entries of hyperbolicmatrices in PSL(2,R).In the level of the matrix group SL(2,R), we will showthat the signs of traces of hyperbolic elementsplay a very important role to determinethe discreteness of holonomy group of a pair of pants.
DISCRETE PRESENTATIONS OF THE HOLONOMY GROUP OF A ONE-HOLED TORUS
김홍찬 한국수학교육학회 2010 純粹 및 應用數學 Vol.17 No.4
A one-holed torus §(1; 1) is a building block of oriented surfaces. In this paper we formulate the matrix presentations of the holonomy group of a one-holed torus §(1; 1) by the gluing method. And we present an algorithm for deciding the discreteness of the holonomy group of §(1; 1).