• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.851-864
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• 2022

We define a kind of sectional curvature and 𝛿-invariants for statistical manifolds. For statistical submanifolds the sum of the squared mean curvature and the squared dual mean curvature is bounded below by using the 𝛿-invariant. This inequality can be considered as a generalization of the so-called Chen inequality for Riemannian submanifolds.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.285-293
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• 2012

In this paper, we investigate the hypersurface M in a unit sphere with constant k-th mean curvature and two distinct principal curvatures, and characterize such a hypersurface.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.75-85
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• 2003

Let M be 3 Semi-invariant submanifold of codimension 3 with lift-flat normal connection in a complex projective space. Further, if the mean curvature of M is constant, then we prove that M is a real hypersurface of a complex projective space of codimension 2 in the ambient space.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.587-601
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• 2022

We find the characterizations of the curvatures of Legendre curves and magnetic curves in Kenmotsu manifolds with C-parallel and C-proper mean curvature vector fields in the tangent and normal bundles. Finally, an illustrative example is presented.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.29-44
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• 2024

In this paper we consider the existence of rotationally symmetric entire solutions for the prescribed higher mean curvature spacelike equations in Minkowski spacetime. As a first step, we study the associated 0-Dirichlet problems on a ball, and then we prove that all possible solutions can be extended to + ∞. The proof of our main results are based upon the topological degree methods and the standard prolongability theorem of ordinary differential equations.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.159-175
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• 2017

We solve the $Bj{\ddot{o}}rling$ problem for constant mean curvature one surfaces in hyperbolic three-space and in de Sitter three-space. That is, we show that for any regular, analytic (and spacelike in the case of de Sitter three-space) curve ${\gamma}$ and an analytic (timelike in the case of de Sitter three-space) unit vector field N along and orthogonal to ${\gamma}$, there exists a unique (spacelike in the case of de Sitter three-space) surface of constant mean curvature 1 which contains ${\gamma}$ and the unit normal of which on ${\gamma}$ is N. Some of the consequences are the planar reflection principles, and a classification of rotationally invariant CMC 1 surfaces.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1435-1458
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• 2018

In this paper, we would like to give an answer to Problem 1 below issued firstly in [17]. In fact, by imposing some conditions on the mean curvature of the initial hypersurface and the coefficient function of the forcing term of a forced mean curvature flow considered here, we can obtain that the first eigenvalues of the Laplace and the p-Laplace operators are monotonic under this flow. Surprisingly, during this process, we get an interesting byproduct, that is, without any complicate constraint, we can give lower bounds for the first nonzero closed eigenvalue of the Laplacian provided additionally the second fundamental form of the initial hypersurface satisfies a pinching condition.

• Kyungpook Mathematical Journal
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• v.52 no.1
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• pp.49-59
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• 2012

In this article, using the example of C. Camci([7]) we reconfirm necessary sufficient condition for a slant curve. Next, we find some necessary and sufficient conditions for a slant curve in a Sasakian 3-manifold to have: (i) a $C$-parallel mean curvature vector field; (ii) a $C$-proper mean curvature vector field (in the normal bundle).

• Proceedings of the KSRS Conference
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• 2002.10a
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• pp.54-58
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• 2002

Mean curvature diffusion (MCD) is a selective smoothing technique that promotes smoothing within a region instead of smoothing across boundaries. By using mean curvature diffusion, noise is eliminated and edges are preserved. In this paper, we propose methods of automatic parameter selection and implementation for the MCD model coupled to min/max flow. The algorithm has been applied to high resolution aerial images and the results show that noise is eliminated and edges are preserved after removal of noise.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.36-51
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• 2022

We study the translation surfaces in the pseudo-Galilean space with the condition that one of generating curves is planar. We classify these surfaces whose mean and Gaussian curvatures are functions of one variable.