Results 1 to 10 of about 654,693 (352)
Existence of mean curvature flow singularities with bounded mean curvature [PDF]
Duke Mathematical Journal, 2020 In [Vel94], Velazquez constructed a countable collection of mean curvature flow solutions in $\mathbb{R}^N$ in every dimension $N \ge 8$. Each of these solutions becomes singular in finite time at which time the second fundamental form blows up.
M. Stolarski
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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
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Self-Expanders of the Mean Curvature Flow [PDF]
Vietnam Journal of Mathematics, 2020 We study self-expanding solutions M m ⊂ ℝ n $M^{m}\subset \mathbb {R}^{n}$ of the mean curvature flow. One of our main results is, that complete mean convex self-expanding hypersurfaces are products of self-expanding curves and flat subspaces, if and ...
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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The hyperbolic mean curvature flow
Journal de Mathématiques Pures et Appliquées, 2007 26 ...
Philippe G. LeFloch, Knut Smoczyk
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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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Non-local interaction in discrete Ricci curvature-induced biological aggregation [PDF]
Royal Society Open ScienceWe investigate the collective dynamics of multi-agent systems in two- and three-dimensional environments generated by minimizing discrete Ricci curvature with local and non-local interaction neighbourhoods.
Jyotiranjan Beuria, Laxmidhar Behera
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Effects of pedicle subtraction osteotomy on aortic morphology and hemodynamics in ankylosing spondylitis with kyphosis: a finite element analysis study [PDF]
Scientific ReportsOsteotomy can correct kyphosis, restore the spinal sequence, and restore the healthy appearance of a patient. However, the aorta is stretched during pedicle subtraction osteotomy (PSO), and some surgeons are concerned about aortic injury.
Weiran Hu +5 more
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Inverse mean curvature flow and Ricci-pinched three-manifolds [PDF]
Journal für die Reine und Angewandte Mathematik, 2023 Let ( M , g ) (M,g) be a noncompact, connected, complete Riemannian three-manifold with nonnegative Ricci curvature satisfying Ric ≥ ε tr ( Ric ) g \mathrm{Ric}\geq\varepsilon\operatorname{tr}(\mathrm{Ric})g for some ε > 0 \varepsilon>0 .
G. Huisken, T. Koerber
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Weak-strong uniqueness for volume-preserving mean curvature flow [PDF]
Revista matemática iberoamericana, 2022 In this note, we derive a stability and weak-strong uniqueness principle for volume-preserving mean curvature flow. The proof is based on a new notion of volume-preserving gradient flow calibrations, which is a natural extension of the concept in the ...
Tim Laux
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