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Convergence rate of the weighted conformal mean curvature flow
Analysis and Geometry in Metric SpacesIn this article, we study the convergence rate of the following Yamabe-type flow Rϕ(t)m=0inMand∂∂tg(t)=2(hϕ(t)m−Hϕ(t)m)g(t)∂∂tϕ(t)=m(Hϕ(t)m−hϕ(t)m)on∂M{R}_{\phi \left(t)}^{m}=0\hspace{0.33em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}M\hspace ...
Hamanaka Shota, Tung Ho Pak
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The fractional mean curvature flow
Bruno Pini Mathematical Analysis Seminar, 2020 In this note, we present some recent results in the study of the fractional mean curvature flow, that is a geometric evolution of the boundary of a set whose speed is given by the fractional mean curvature.
Eleonora Cinti
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Pinched hypersurfaces are compact
Advanced Nonlinear Studies, 2023 We make rigorous and old idea of using mean curvature flow to prove a theorem of Richard Hamilton on the compactness of proper hypersurfaces with pinched, bounded curvature.
Bourni Theodora +2 more
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Nonlocal diffusion of smooth sets
Mathematics in Engineering, 2022 We consider normal velocity of smooth sets evolving by the $ s- $fractional diffusion. We prove that for small time, the normal velocity of such sets is nearly proportional to the mean curvature of the boundary of the initial set for $ s\in [\frac{1}{2},
Anoumou Attiogbe +2 more
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Non-Parametric Mean Curvature Flow with Prescribed Contact Angle in Riemannian Products
Analysis and Geometry in Metric Spaces, 2022 Assuming that there exists a translating soliton u∞ with speed C in a domain Ω and with prescribed contact angle on ∂Ω, we prove that a graphical solution to the mean curvature flow with the same prescribed contact angle converges to u∞ + Ct as t →∞.
Casteras Jean-Baptiste +3 more
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Curvature-based interface restoration algorithm using phase-field equations.
PLoS ONE, 2023 In this study, we propose a restoration algorithm for distorted objects using a curvature-driven flow. First, we capture the convex-hull shaped contour of the distorted object using the mean curvature flow.
Seunggyu Lee, Yongho Choi
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Life-Span of Classical Solutions to Hyperbolic Inverse Mean Curvature Flow
Discrete Dynamics in Nature and Society, 2020 In this paper, we investigate the life-span of classical solutions to hyperbolic inverse mean curvature flow. Under the condition that the curve can be expressed in the form of a graph, we derive a hyperbolic Monge–Ampère equation which can be reduced to
Zenggui Wang
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Recent rigidity results for graphs with prescribed mean curvature
Mathematics in Engineering, 2021 This survey describes some recent rigidity results obtained by the authors for the prescribed mean curvature problem on graphs u : M → R. Emphasis is put on minimal, CMC and capillary graphs, as well as on graphical solitons for the mean curvature flow ...
Bruno Bianchini +5 more
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Forced hyperbolic mean curvature flow [PDF]
, 2012 In this paper, we investigate two hyperbolic flows obtained by adding forcing terms in direction of the position vector to the hyperbolic mean curvature flows in \cite{klw,hdl}.
Mao, Jing
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A remark on soliton equation of mean curvature flow
Anais da Academia Brasileira de Ciências, 2004 In this note, we consider self-similar immersions of the mean curvature flow and show that a graph solution of the soliton equation, provided it has bounded derivative, converges smoothly to a function which has some special properties (see Theorem 1.1 ...
Li Ma, Yang Yang
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