• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.129-137
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• 2007

It is known that connectedness is one of the important notions in topology. In this paper, a new notion of connectedness is introduced in L-topological spaces, which is called PS-connectedness. It contains some nice properties. Especially, the famous K. Fan's Theorem holds for PS-connectedness in L-topological spaces.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.109-127
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• 2007

We classify complete, locally homogeneous metrics with finite volume on four-dimensional manifolds which are critical points for the squared $L^2-norm$ functionals of either the full Riemannian curvature tensor or the Weyl curvature tensor defined on the space of Riemannian metrics.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1185-1195
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• 2007

We will discuss some very old and some new open problems concerning infinite dimensional algebras. All these problems have been inspired by combinatorial group theory.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1093-1102
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• 2007

In this note we survey some recent results on symmetric space, and related topics like rigidity, flexibility and geometry-topology aspect of symmetric space, specially in the line of hyperbolic 3-manifolds.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1051-1063
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• 2007

The aim of this note is to advertise a method which turns out to be powerful enough to be used successfully in problems which are apparently unrelated. It is based on a modification of a construction that we first introduced in [2].

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.831-867
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• 2003

In this paper, we find the unitary dual of the group SL(2,R)(equation omitted)R($^{m,2}$) and study automorphic forms related to the group SL(2,R)(equation omitted)R($^{m, 2}$).).

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.821-838
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• 2015

We investigate the relative and Tate cohomology theories with respect to Ding modules and complexes, consider their relations with classical and Gorenstein cohomology theories. As an application, the Avramov-Martsinkovsky type exact sequence of Ding modules is obtained.

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.699-725
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• 2015

In this paper, we study the estimation for algebraic polynomials in the bounded and unbounded regions bounded by piecewise Dini smooth curve having interior and exterior zero angles.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.733-748
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• 2017

We give Hodge structures on quasitoric orbifolds. We define orbifold Hodge numbers and show a correspondence of orbifold Hodge numbers for crepant resolutions of quasitoric orbifolds. In short we extend Hodge structures to a non almost complex setting.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.763-772
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• 2017

In this paper, we study the Liouville type theorems for transversally harmonic and biharmonic maps on foliated Riemannian manifolds.