Byung-Kun Oh
Hanyang University · Mathematics
About the Lab
Professor Byung-Kun Oh's research spans diverse areas in mathematical physics and theoretical mathematics, with a strong focus on geometric analysis, complex analysis, and discrete geometry. His work explores the interplay between curvature, conformal structures, and combinatorial properties in Riemann surfaces, disk triangulation graphs, and planar graphs. He investigates fundamental geometric classifications such as circle packing types and Gromov hyperbolicity, often using both geometric and combinatorial methods. His research also includes applications to mathematical physics, including the study of Aleksandrov surfaces and Nevanlinna theory.
Research Overview
Research Output Trend
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Selected Papers
14本研究はフェーン現象下の気象を風洞装置を用いて再現し, 高温乾燥風に対する耐性イネ品種と感受性品種との水分状態とクロロフィル含量の差を調べたものである. 耐性品種として韓国農村振興庁嶺南農業試験場の盈徳出張所で選抜した日本型Naepung-byeo (NP), 感受性品種として同定されたオーストラリア原産の日本型Ilabong (IB) を供試し, それぞれ水田土壌をつめた1/1250aポットに移植し, 屋外自然条件下の湛水状態で生育させた. 3時間の高温乾燥風処理は出穂後4日目に行った. 穂の水ポテンシャルの変化は処理終了直後から顕著に現れ, NPでは処理開始前の-0.25 MPaに比べ, -0.75 MPaと大きく低下した. 一方, IBではさらに著しく, 処理開始前の-0.34 MPaから-1.53 MPaに大きく低下した. NPの穂の水ポテンシャルは, 処理終了後2時間目までは低下したが, 処理終了後6時間目には回復する傾向を示した. 葉身における水ポテンシャルは低下する傾向があったものの, 高温乾燥風処理による差は小さく, 品種間で有意な差は認められなかった. また, 穂の相
Aleksandrov surfaces are a generalization of two-dimensional Riemannian manifolds, and it is known that every open simply-connected Aleksandrov surface is conformally equivalent either to the unit disc (hyperbolic case) or to the plane (parabolic case). We prove a criterion for hyperbolicity of Aleksandrov surfaces which have <italic>nice</italic> tilings and where negative curvature dominates. We then apply this to generalize a result of Nevanlinna and give a partial answer for his conjecture a
We investigate criteria for circle packing (CP) types of disk triangulation graphs embedded into simply connected domains in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper C"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">C</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathbb {C}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . In parti
In this paper we describe how to define the circle packing (cp) type (either cp parabolic or cp hyperbolic) of a Riemann surface of class S, and study the relation between this type and the conformal type of the surface.
We study the relations between strong isoperimetric inequalities and Gromov hyperbolicity on planar graphs, and give an alternative proof for the following statement: if a planar graph of bounded face degree satisfies a strong isoperimetric inequality, then it is Gromov hyperbolic. This theorem was formerly proved in the author's paper from 2014 [12] using combinatorial methods, while geometric approach is used in the present paper.
We study the relations between strong isoperimetric inequalities and Gromov hyperbolicity on planar graphs, and give an alternative proof for the following statement: if a planar graph of bounded face degree satisfies a strong isoperimetric inequality, then it is Gromov hyperbolic. This theorem was formerly proved in the author’s paper from 2014 [12] using combinatorial methods, while geometric approach is used in the present paper.
We provide sharp bounds for the isoperimetric constants of infinite plane\ngraphs (tessellations) with bounded vertex and face degrees. For example, if\n$G$ is a plane graph satisfying the inequalities $p_1 \\leq \\mbox{deg}\\ v \\leq\np_2$ for $v \\in V(G)$ and $q_1 \\leq \\mbox{deg}\\ f \\leq q_2$ for $f \\in F(G)$,\nwhere $p_1, p_2, q_1$, and $q_2$ are natural numbers such that $1/p_i + 1/q_i\n\\leq 1/2$, $i=1,2$, then we show that \\[ \\Phi (p_1, q_1) \\leq \\inf_S\n\\frac{|\\partial S|}{|V(
This paper is about hyperbolic properties on planar graphs. First, we study\nthe relations among various kinds of strong isoperimetric inequalities on\nplanar graphs and their duals. In particular, we show that a planar graph\nsatisfies a strong isoperimetric inequality if and only if its dual has the\nsame property, if the graph satisfies some minor regularity conditions and we\nchoose an appropriate notion of strong isoperimetric inequalities. Second, we\nconsider planar graphs where negative
We give a criterion for vertex extremal length parabol- icity of locally finite planar graphs, and use it to show that a disk triangulation graph is circle packing parabolic if and only if its im- mediate finer graphs are circle packing parabolic.
An Aleksandrov surface is a generalization of two-dimensional Riemannian manifolds, and it is known by a theorem of A. Huber (1960) that every open simply connected Aleksandrov surface is conformally equivalent either to the unit disc (hyperbolic case) or to the plane (parabolic case). Thus one can study complex analysis on Aleksandrov surfaces, and in the first part of this thesis we prove a criterion for hyperbolicity of an Aleksandrov surface which has a nice tiling (or triangulation) and for
Research Areas
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