• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.485-498
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• 2005

In this article we show that every quasi-homogeneous convex affine domain whose boundary is everywhere differentiable except possibly at a finite number of points is either homogeneous or covers a compact affine manifold. Actually we show that such a domain must be a non-elliptic strictly convex cone if it is not homogeneous.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.113-120
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• 2001

Using the notions of admissibility, local convexity and measure of noncompactness, we give new fixed point theorems for quasicompact or condensing multivalued mappings with domains that are not necessarily convex subsets of an arbitrary topological vector space.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.513-527
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• 2015

In this paper, we first introduce and study new concepts of ($k_1,{\cdots},k_n$)-convexity and k-segment. Secondly, we shall discuss some properties of nonisotropically starlike domains in $\mathbb{R}^n$ with respect to the origin.

• East Asian mathematical journal
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• v.25 no.2
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• pp.221-227
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• 2009

In this paper, we introduce the generalized H$\ddot{o}$lder space with a majorant function and prove the H$\ddot{o}$lder regularity for solutions of the Cauchy-Riemann equation in the generalized Holder spaces on a bounded convex domain in $\mathbb{C}^2$.

• East Asian mathematical journal
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• v.17 no.1
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• pp.159-165
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• 2001

• Journal of the Korean Mathematical Society
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• v.37 no.2
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• pp.253-267
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• 2000

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.171-177
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• 1993

In this paper, we show that Greene-Krantz's conjecture is true for certain class of domains. In fact, we give a complete classification of automorphism groups of domains of the form (Fig.) where the function .phi. is a real valued $C^{\infty}$ function in a neighborhood of [0,1] which satisfies the following conditions; (1) .phi.(0)=.phi.'(0)=0 and .phi.(1)=1, (2) .phi.(t) is increasing and convex for t>0.vex for t>0.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.487-493
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• 2001

$Let \Omega$ be a bounded convex domain in C^n$ with smooth boundary. Let M be a subvariety of $\Omega$ which intersects $\partial$$\Omega$ transversally. Suppose that $\Omega$ is totally convex at any point of $\partial$M in the complex tangential directions.For f $\epsilon$O(M)$\bigcap$/TEX>$C^{\infty}$($\overline{M}$/TEX>), there exists F $\epsilon$ o ($\Omega$))$\bigcap$/TEX>$C^{\infty}$($\overline{\Omega}$/TEX>) such that F(z) = f(z) for z $\epsilon$ M.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.11
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• pp.1003-1011
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• 2013

A new formulation of the MNDIF method is introduced to extract highly accurate eigenvalues of concave acoustic cavities. Since the MNDIF method, which was introduced by the author, can be applicable for only convex acoustic cavities, a new approach of dividing a concave cavity into two convex domains and formulating an algebraic eigenvalue problem is proposed in the paper. A system matrix equation, which gives eigenvalues, is obtained from boundary conditions for each domain and the condition of continuity in the interface between the two domains. The validity and accuracy of the proposed method are shown through example studies.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.165-173
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• 2017

In this paper, we prove that the automorphism group of a quasi-homogeneous properly convex affine domain in ${\mathbb{R}_n}$ acts transitively on the set of all the extreme points of the domain. This set is equal to the set of all the asymptotic cone points coming from the asymptotic foliation of the domain and thus it is a homogeneous submanifold of ${\mathbb{R}_n}$.