• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.809-820
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• 2004

On $R^{2n}$, n$\geq$2, with the standard symplectic structure we construct compatible almost K hler metrics with negative scalar curvature on a polydisc which are Euclidean away from the polydisc.c.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.977-991
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• 2012

Let (M,F) and (M',F') be two foliated Riemannian manifolds with M compact. If the transversal Ricci curvature of F is nonnegative and the transversal sectional curvature of F' is nonpositive, then any transversally harmonic map ${\phi}:(M,F){\rightarrow}(M^{\prime},F^{\prime})$ is transversally totally geodesic. In addition, if the transversal Ricci curvature is positive at some point, then ${\phi}$ is transversally constant.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.817-824
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• 2017

In this paper, we prove that a gradient shrinking Ricci soliton is rigid if the radial curvature vanishes and the second order divergence of Bach tensor is non-positive. Moreover, we show that a complete non-compact gradient expanding Ricci soliton is rigid if the radial curvature vanishes, the Ricci curvature is nonnegative and the second order divergence of Bach tensor is nonnegative.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1539-1561
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• 2021

We prove Perelman type 𝒲-entropy formulae and differential Harnack estimates for positive solutions to weighed doubly nonlinear diffusion equation on weighted Riemannian manifolds with CD(-K, m) condition for some K ≥ 0 and m ≥ n, which are also new for the non-weighted case. As applications, we derive some Harnack inequalities.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.1023-1041
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• 2023

In this paper, motivated by the work of Q. S. Zhang in [25], we derive optimal Li-Yau gradient bounds for positive solutions of the f-heat equation on closed manifolds with Bakry-Émery Ricci curvature bounded below.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1311-1332
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• 2013

This paper concerns the evolution of a closed hypersurface of the hyperbolic space, convex by horospheres, in direction of its inner unit normal vector, where the speed equals a positive power ${\beta}$ of the positive mean curvature. It is shown that the flow exists on a finite maximal interval, convexity by horospheres is preserved and the hypersurfaces shrink down to a single point as the final time is approached.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.601-603
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• 2013

We show that a compact embedded hypersurface with constant ratio of mean curvature functions in a convex cone $C{\subset}\mathbb{R}^{n+1}$ is part of a hypersphere if it has a point where all the principal curvatures are positive and if it is perpendicular to ${\partial}C$.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.561-570
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• 2021

In this paper, applying the bifurcation method and topological analysis, we investigate the global structures of solutions for one-dimensional Minkowski-curvature problems under certain behavior of nonlinear term near zero.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.3
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• pp.846-857
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• 1995

An experimental study is made of turbulent shear flows in a nearly two-dimensional 90.deg. curved duct by using the hot-wire anemometer. The Reynolds normal and shear stresses, triple velocity products, integral length scales, Taylor micro length scales and dissipation length scales are measured and analyzed. For a positive shear at the inlet, the afore-mentioned turbulence quantities are all suppressed. However, when the inlet shear flow is negative, they are augmented, i.e., the convex curvature suppresses the turbulence whereas the concave curvature augments it. It is found that the curvature effects are rather sensitive to the triple velocity products than the Reynolds stresses. The evolution of turbulence under the curvature with the different shear conditions is well described by the modified curvature parameter S' and the non-dimensional development time ${\tau}$.'

• Journal of the Korean Mathematical Society
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• v.28 no.1
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• pp.87-97
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• 1991