Results 31 to 40 of about 5,400,024 (317)
Remarks on mean curvature flow solitons in warped products [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2018 We study some properties of mean curvature flow solitons in general Riemannian manifolds and in warped products, with emphasis on constant curvature and Schwarzschild type spaces.
G. Colombo, L. Mari, M. Rigoli
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The mean curvature at the first singular time of the mean curvature flow
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2010 Consider a family of smooth immersions F( \cdot ,t):M^{n}\rightarrow \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} = −
Nam Q. Le, Natasa Sesum
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Bubbles with constant mean curvature, and almost constant mean curvature, in the hyperbolic space [PDF]
Calculus of Variations and Partial Differential Equations, 2021 AbstractGiven a constant $$k>1$$ k > 1 , let Z be the family of round spheres of radius $${{\,\mathrm{artanh}\,}}(k^{-1})$$ artanh
G. Cora, R. Musina
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Mean curvature flow with obstacles
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. Assuming the regularity of the obstacles, in the two-dimensional case we show existence and uniqueness of a regular solution before the ...
Almeida, Luís +2 more
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On the evolution by fractional mean curvature [PDF]
Communications in Analysis and Geometry, 2019 In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish evolutions equations for fractional geometric quantities that yield preservation of certain quantities (such as positive ...
Sáez, Mariel, Valdinoci, Enrico
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Constant mean curvature surfaces [PDF]
Surveys in Differential Geometry, 2016 In this article we survey recent developments in the theory of constant mean curvature surfaces in homogeneous 3-manifolds, as well as some related aspects on existence and descriptive results for $H$-laminations and CMC foliations of Riemannian $n$-manifolds.
H. Meeks III, William +2 more
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Convergence of the Allen‐Cahn Equation to Multiphase Mean Curvature Flow [PDF]
, 2016 We present a convergence result for solutions of the vector‐valued Allen‐Cahn equation. In the spirit of the work of Luckhaus and Sturzenhecker we establish convergence towards a distributional formulation of multiphase mean~curvature flow using sets of ...
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The space of asymptotically conical self-expanders of mean curvature flow [PDF]
Mathematische Annalen, 2017 We show that the space of asymptotically conical self-expanders of the mean curvature flow is a smooth Banach manifold. An immediate consequence is that non-degenerate self-expanders—that is, those self-expanders that admit no non-trivial normal Jacobi ...
J. Bernstein, Lu Wang
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Nonfattening of Mean Curvature Flow at Singularities of Mean Convex Type [PDF]
Communications on Pure and Applied Mathematics, 2017 We show that a mean curvature flow starting from a compact, smoothly embedded hypersurface M ⊆ ℝn + 1 remains unique past singularities, provided the singularities are of mean convex type, i.e., if around each singular point, the surface moves in one ...
Or Hershkovits, B. White
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Superharmonicity of curvatures for surfaces of constant mean curvature [PDF]
Pacific Journal of Mathematics, 1992 The article deals with the superharmonicity of some curvatures (the scalar curvature \(R\), the Gauss-Kronecker curvature \(K\), the \(\nu\)-th mean curvature \({K}_ \nu\), the level curvature \(L\)) of hypersurfaces of constant mean curvature in \(\mathbb{R}^ n\). For instance, it is proved that for a hypersurface of positive sectional curvatures \(R\)
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