Results 11 to 20 of about 255,201 (317)
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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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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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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Mean curvature flow in a Ricci flow background [PDF]
Communications in Mathematical Physics, 2012 Following work of Ecker, we consider a weighted Gibbons-Hawking-York functional on a Riemannian manifold-with-boundary. We compute its variational properties and its time derivative under Perelman's modified Ricci flow.
B. Kleiner +14 more
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Mean curvature flow without singularities
Journal of Differential Geometry, 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.
Schnürer, Oliver C. +1 more
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The volume preserving mean curvature flow. [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 1987 Let \(F: M^ n\to {\mathbb{R}}^{n+1}\) be the immersion of a uniformly convex closed hypersurface in \({\mathbb{R}}^{n+1}\). \(M^ n\) is deformed by the evolution equation \(\partial F/\partial t=(h-H)\cdot \nu\) where \(\nu\) is the outer unit normal to M, H is the mean curvature and h is the average of H.
Gerhard Huisken
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The hyperbolic mean curvature flow
Journal de Mathématiques Pures et Appliquées, 2007 26 ...
Philippe G. LeFloch, Knut Smoczyk
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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
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Hyperbolic mean curvature flow [PDF]
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
Chun-Lei He, Kefeng Liu, Dexing Kong
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On the extension of the mean curvature flow [PDF]
Mathematische Zeitschrift, 2009 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 $\frac{\partial F(p,t)}{\partial t} = -H(p,t)\cdot (p,t)$, for $t\in [0,T)$. In \cite{Cooper} Cooper has recently proved that the mean curvature blows up at the singular time $T$. We show that if
Nam Q. Le, Nataša Šešum
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