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Mean curvature flow [PDF]

Bulletin of the American Mathematical Society, 2014
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
Colding, Tobias, Minicozzi, William, Pedersen, Erik J   +2 more
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Mean Curvature Flow on Ricci Solitons [PDF]

Journal of Physics A: Mathematical and Theoretical, 2010
We study monotonic quantities in the context of combined geometric flows. In particular, focusing on Ricci solitons as the ambient space, we consider solutions of the heat type equation integrated over embedded submanifolds evolving by mean curvature ...
Bakas I, Cao H D Zhu X P, Chow B, Efstratios Tsatis, Fateev V A Onofri E, Hamilton R, Huisken G, Kleiner B Lott J, Mantegazza C Magni A Tsatis E, Morgan J Tian G, Ni L, Perelman G, Perelman G, Perelman G, Zamolodchikov A B, Zamolodchikov A B   +15 more
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Topological Change in Mean Convex Mean Curvature Flow [PDF]

Inventiones mathematicae, 2013
Consider the mean curvature flow of an (n+1)-dimensional, compact, mean convex region in Euclidean space (or, if ...
A. Hatcher, A. Stone, B. White, B. White, B. White, B. White, Brian White, G. Huisken, L.C. Evans, S. Altschuler, T. Ilmanen, T. Ilmanen   +11 more
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Convergence rate of the weighted conformal mean curvature flow

Analysis and Geometry in Metric Spaces
In 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
doaj   +2 more sources

Gaussian mean curvature flow [PDF]

Journal of Evolution Equations, 2010
10 ...
Borisenko, Alexander A., Miquel, Vicente
openaire   +2 more sources

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
openaire   +4 more sources

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
doaj   +1 more source

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, Langford Mat, Lynch Stephen   +2 more
doaj   +1 more source

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, Heinonen Esko, Holopainen Ilkka, De Lira Jorge H.   +3 more
doaj   +1 more source

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
doaj   +1 more source