Results 51 to 60 of about 654,693 (352)
Guan–Li type mean curvature flow for free boundary hypersurfaces in a ball [PDF]
Communications in analysis and geometry, 2019 In this paper we introduce a Guan-Li type volume preserving mean curvature flow for free boundary hypersurfaces in a ball. We give a concept of star-shaped free boundary hypersurfaces in a ball and show that the Guan-Li type mean curvature flow has long ...
Guofang Wang, C. Xia
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Singularity Profile in the Mean Curvature Flow [PDF]
Methods and Applications of Analysis, 2009 In this paper we study the geometry of first time singularities of the mean curvature flow. By the curvature pinching estimate of Huisken and Sinestrari, we prove that a mean curvature flow of hypersurfaces in the Euclidean space $\R^{n+1}$ with positive mean curvature is $ $-noncollapsing, and a blow-up sequence converges locally smoothly along a ...
Sheng, Weimin, Wang, Xu-Jia
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A note on Alexandrov immersed mean curvature flow [PDF]
arXiv, 2022 We demonstrate that the property of being Alexandrov immersed is preserved along mean curvature flow. Furthermore, we demonstrate that mean curvature flow techniques for mean convex embedded flows such as noncollapsing and gradient estimates also hold in this setting. We also indicate the necessary modifications to the work of Brendle--Huisken to allow
arxiv
A finite element error analysis for axisymmetric mean curvature flow [PDF]
arXiv.org, 2019 We consider the numerical approximation of axisymmetric mean curvature flow with the help of linear finite elements. In the case of a closed genus-1 surface, we derive optimal error bounds with respect to the $L^2$-- and $H^1$--norms for a fully discrete
J. Barrett, K. Deckelnick, R. Nürnberg
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Is mean curvature flow a gradient flow?
, 2023 It is well-known that the mean curvature flow is a formal gradient flow of the perimeter functional. However, by the work of Michor and Mumford [7,8], the formal Riemannian structure that is compatible with the gradient flow structure induces a degenerate metric on the space of hypersurfaces.
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Extend Mean Curvature Flow with Finite Integral Curvature [PDF]
Asian Journal of Mathematics, 2011 In this note, we first prove that the solution of mean curvature flow on a finite time interval $[0,T)$ can be extended over time $T$ if the space-time integration of the norm of the second fundamental form is finite. Secondly, we prove that the solution of certain mean curvature flow on a finite time interval $[0,T)$ can be extended over time $T$ if ...
Xu, Hong-Wei, Ye, Fei, Zhao, En-Tao
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A Comparison Principle for the Mean Curvature Flow Equation with Discontinuous Coefficients
International Journal of Differential Equations, 2016 We study the level set equation in a bounded domain when the velocity of the interface is given by the mean curvature plus a discontinuous velocity. We prove a comparison principle for the initial-boundary value problem whose consequence is uniqueness of
Cecilia De Zan, Pierpaolo Soravia
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Nguyen’s tridents and the classification of semigraphical translators for mean curvature flow [PDF]
Journal für die Reine und Angewandte Mathematik, 2019 We construct a one-parameter family of singly periodic translating solutions to mean curvature flow that converge as the period tends to 0 to the union of a grim reaper surface and a plane that bisects it lengthwise.
D. Hoffman, F. Mart'in, B. White
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Singular perturbations of mean curvature flow
Journal of Differential Geometry, 2007 We introduce a regularization method for mean curvature flow of a submanifold of arbitrary codimension in the Euclidean space, through higher order equations. We prove that the regularized problems converge to the mean curvature flow for all times before the first singularity.
GIOVANNI BELLETTINI +2 more
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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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