Results 11 to 20 of about 133,968 (310)
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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Concentrated Curvature for Mean Curvature Estimation in Triangulated Surfaces [PDF]
, 2012 We present a mathematical result that allows computing the discrete mean curvature of a polygonal surface from the so-called concentrated curvature generally used for Gaussian curvature estimation. Our result adds important value to concentrated curvature as a geometric and metric tool to study accurately the morphology of a surface.
M. M. Mesmoudi +2 more
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Spectral Prescribed Mean Curvature
CoRRWe consider prescribed mean curvature equations whose solutions are minimal surfaces, constant mean curvature surfaces, or capillary surfaces. We consider both Dirichlet boundary conditions for Plateau problems and nonlinear Neumann boundary conditions for capillary problems and we consider domains in $\mathbf{R}^2$ to be rectangles, disks, or annuli.
Jonas Haug, Rachel Jewell, Ray Treinen
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Approximations of the mean curvature, and the Buet-Rumpf approximate mean curvature flow
CoRRThe aim of this paper is to generalize the work of B. Buet and M. Rumpf on some definition of the approximate mean curvature vector for varifolds, and its associated mean curvature motions for points clouds. We propose a generalization of the definition of the approximate mean curvature vector in two terms: in terms of linear operators and in terms of ...
Sagueni, Abdelmouksit
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Constant Mean Curvature Surfaces Along a Spacelike Curve
Cumhuriyet Science Journal, 2022 We construct constant mean curvature surfaces along a given spacelike curve in 3 dimensional Minkowski space. We parametrically present these surfaces using the famous Frenet frame of the curve in question.
Ergin Bayram
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Lagrangian mean curvature flow [PDF]
, 2021 Lagrangian mean curvature flow is a powerful tool in modern mathematics with connections to topics in analysis, geometry, topology and mathematical physics.
Lotay, Jason D.
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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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Mean Curvature Dictates the Diffusion of Lipids Along Curved Membranes
, 2023 Curved cellular membranes are both abundant and functionally relevant. While novel tomography approaches reveal the structural details of curved membranes, their dynamics pose an experimental challenge.
Balázs, Fábián, Matti, Javanainen
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Hyperbolic inverse mean curvature flow [PDF]
, 2020 summary:We prove the short-time existence of the hyperbolic inverse (mean) curvature flow (with or without the specified forcing term) under the assumption that the initial compact smooth hypersurface of $\mathbb {R}^{n+1}$ ($n\ge 2$) is mean convex and ...
Zhou, Zhe, Mao, Jing, Wu, Chuan-Xi
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