Results 1 to 10 of about 564,094 (221)
The hyperbolic mean curvature flow [PDF]
Journal de Mathématiques Pures et Appliquées, 2007 We introduce a geometric evolution equation of hyperbolic type, which governs the evolution of a hypersurface moving in the direction of its mean curvature vector.
LeFloch, Philippe G., Smoczyk, Knut
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Mean curvature flow without singularities [PDF]
arXiv, 2012 We study graphical mean curvature flow of complete solutions defined on subsets of Euclidean space. We obtain smooth long time existence. The projections of the evolving graphs also solve mean curvature flow. Hence this approach allows to smoothly flow through singularities by studying graphical mean curvature flow with one additional dimension.
Schnürer, Oliver C. +1 more
arxiv +10 more sources
Mean curvature flow with obstacles [PDF]
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2012 We consider the evolution of fronts by mean curvature in the presence of obstacles. We construct a weak solution to the flow by means of a variational method, corresponding to an implicit time-discretization scheme.
Almeida, Luís +2 more
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A remark on soliton equation of mean curvature flow [PDF]
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
doaj +2 more sources
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 +2 more
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The mean curvature at the first singular time of the mean curvature flow [PDF]
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2010 Consider a family of smooth immersions $F(\cdot,t): M^n\to \mathbb{R}^{n+1}$ of closed hypersurfaces in $\mathbb{R}^{n+1}$ moving by the mean curvature flow $\frac{\partial F(p,t)}{\partial t} = -H(p,t)\cdot \nu(p,t)$, for $t\in [0,T)$. We prove that the
Brakke +26 more
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Mean curvature flow and Riemannian submersions [PDF]
Geometriae Dedicata, 2015 We give a sufficient condition ensuring that the mean curvature flow commutes with a Riemannian submersion and we use this result to create new examples of evolution by mean curvature flow.
Pipoli, Giuseppe
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Universality in mean curvature flow neckpinches [PDF]
Duke Mathematical Journal, 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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Width and mean curvature flow [PDF]
Geometry & Topology, 2007 Given a Riemannian metric on a homotopy $n$-sphere, sweep it out by a continuous one-parameter family of closed curves starting and ending at point curves. Pull the sweepout tight by, in a continuous way, pulling each curve as tight as possible yet preserving the sweepout.
Tobias Colding, William P. Minicozzi
openalex +6 more sources
Forced hyperbolic mean curvature flow [PDF]
Kodai Mathematical Journal, 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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