• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.841-852
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• 2019

We establish the generalized Myers theorem for Finsler manifolds under integral Ricci curvature bound. More precisely, we show that the forward complete Finsler n-manifold whose part of Ricci curvature less than a positive constant is small in $L^p$-norm (for p > n/2) have bounded diameter and finite fundamental group.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.45 no.4
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• pp.68-78
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• 2008

For a smooth transition between consecutive paths, conventional robot controllers usually generate a transition trajectory by blending consecutive paths in a time coordinate. However, this has two inherent drawbacks: the shape of a transition path cannot be designed coherently and the speed during transition is uncontrollable. To overcome these problems, this paper provides a path-level, rather than trajectory-level, smooth transition method with the curvature bound between non-smoothly connected paths. The experiment results show that the resultant transition trajectory is more smoothly connected than the conventional methods and the curvature is closely limited to the desired bound within the guaranteed level ($0.02{\sim}1$).

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.213-220
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• 2004

In this paper, we generalize the Bishop-Gromov volume comparison theorem by considering an integral bound for the part of the radial Ricci curvature which lies below a given smooth function. We also establish a compactness theorem from this result.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.235-246
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• 2005

We present an interpolating, univariate subdivision scheme which preserves the discrete curvature and tangent direction at each step of subdivision. Since the polygon have a geometric information of some original(in some sense) curve as a discrete curvature, we can expect that the limit curve has the same curvature at each vertex as the control polygon. We estimate the curvature bound of odd vertices and give an error estimate for restoring a curve from sampled vertices on curves.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.833-837
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• 2013

In this note we establish a generalized Myers theorem under line integral curvature bound for Finsler manifolds.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.61-66
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• 2009

We provide a generalized Myers theorem under integral curvature bound and use this result to obtain a closure theorem in general relativity.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.677-683
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• 2008

On a compact n-dimensional manifold M, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of volume 1, should be Einstein. The purpose of the present paper is to prove that a 3-dimensional manifold (M,g) is isometric to a standard sphere if ker $s^*_g{{\neq}}0$ and there is a lower Ricci curvature bound. We also study the structure of a compact oriented stable minimal surface in M.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.39-44
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• 2005

Let M be a compact hypersurface in hyperbolic space and let A be the area of M and V be the volume of the compact domain bounded by M. In this paper, we find a lower bound for $\frac{A}{V}$ in two cases, M has constant scalar curvature and M has constant mean curvature.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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• pp.369-378
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• 2021

In this paper, we give an upper bound for the fundamental tone of stable constant mean curvature hypersurfaces in hyperbolic space. Let M be an n-dimensional complete non-compact constant mean curvature hypersurface with finite L²-norm of the traceless second fundamental form. If M is weakly stable, then λ₁(M) is bounded above by n² + O(n^2+s) for arbitrary s > 0.

• Transactions of Materials Processing
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• v.7 no.2
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• pp.177-185
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• 1998

The kinematically admissible veolcity field is developed for the shapes of dead metal zone and the curving velocity distribution in the eccentric plane dies extrusion. The shape of dead metal zone is defined as the boundary surface with the maximum friction constant between the deformable zone and the rigid zone. The curving phenomenon in the eccentric lane dies is caused by the eccentricity of plane dies. The axial velocity distribution in the plane dies is divided in to the uniform velocity and the deviated velocity. The deviated velocity is linearly changed with the distance from the center of cross-section of the workpiece. The results show that the curvature of products and the shapes of the dead metal one are determined by the minimization of the plastic work and that the curvature of the extruded products increase with the eccentricity.