Results 11 to 20 of about 528,992 (279)
Spacelike Mean Curvature Flow [PDF]
The Journal of Geometric Analysis, 2019 AbstractWe prove long-time existence and convergence results for spacelike solutions to mean curvature flow in the pseudo-Euclidean space$$\mathbb {R}^{n,m}$$Rn,m, which are entire or defined on bounded domains and satisfying Neumann or Dirichlet boundary conditions. As an application, we prove long-time existence and convergence of the$${{\,\mathrm{G}\
Ben Lambert, Jason D. Lotay
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Special Curves in Engineering. Surfaces Generated by the Logarithmic Spiral
Modelling in Civil Environmental Engineering, 2022 The logarithmic spiral is one of the most known curves with applications in engineering. We consider product of the logarithmic spiral with a real line and tensor product of two logarithmic spirals and investigate their minimality or flatness.
Broscăţeanu Ștefan Cezar
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Stability of helicoidal surfaces with constant mean curvature
International Journal of Mathematics for Industry, 2020 Motivated by an experimental result on the shape of liquid water supported by a small stainless helical wire, we find a class of stable helicoidal convex surfaces with constant mean curvature whose boundary consists of a single helix and two short arcs.
Yuta Hatakeyama, Miyuki Koiso
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Lietuvos Matematikos Rinkinys, 2010 In this article we generalize some classical formulas for curvatures of hypersurfaces in the n-dimensional Euclidean space using the homogeneous formulas.
Kazimieras Navickis
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On Total Shear Curvature of Surfaces in E^{n+2}
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2018 In the present study we consider surfaces in Euclidean (n+2)-space Eⁿ⁺². Firstly, we introduce some basic concepts of second fundamental form and curvatures of the surfaces in Eⁿ⁺².
Kadri Arslan, Betül Bulca
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Universality in mean curvature flow neckpinches [PDF]
, 2014 We study noncompact surfaces evolving by mean curvature flow. Without any symmetry assumptions, we prove that any solution that is $C^3$-close at some time to a standard neck will develop a neckpinch singularity in finite time, will become asymptotically
Gang, Zhou, Knopf, Dan
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Examples of surfaces of constant mean curvature
Дифференциальная геометрия многообразий фигур, 2019 A surface in E3 is called parallel to the surface M if it consists of the ends of constant length segments, laid on the normals to the surfaces at points of this surface. The tangent planes at the corresponding points will be parallel.
M. A. Cheshkova
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Hyperbolic mean curvature flow
Journal of Differential Equations, 2009 In this paper we introduce the hyperbolic mean curvature flow and prove that the corresponding system of partial differential equations are strictly hyperbolic, and based on this, we show that this flow admits a unique short-time smooth solution and possesses the nonlinear stability defined on the Euclidean space with dimension larger than 4. We derive
He, Chun-Lei, Kong, De-Xing, Liu, Kefeng
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Bulletin of the American Mathematical Society, 2015 Mean curvature flow is the negative gradient flow of volume, so any hypersurface flows through hypersurfaces in the direction of steepest descent for volume and eventually becomes extinct in finite time. Before it becomes extinct, topological changes can occur as it goes through singularities. If the hypersurface is in general or generic position, then
Colding, Tobias +2 more
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Circulant preconditioners for mean curvature-based image deblurring problem
Journal of Algorithms & Computational Technology, 2021 The mean curvature-based image deblurring model is widely used to enhance the quality of the deblurred images. However, the discretization of the associated Euler–Lagrange equations produces a nonlinear ill-conditioned system which affects the ...
Shahbaz Ahmad, Faisal Fairag
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