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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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Diameter Estimate in Geometric Flows
Mathematics, 2023 We prove the upper and lower bounds of the diameter of a compact manifold (M,g(t)) with dimRM=n(n≥3) and a family of Riemannian metrics g(t) satisfying some geometric flows. Except for Ricci flow, these flows include List–Ricci flow, harmonic-Ricci flow,
Shouwen Fang, Tao Zheng
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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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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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Disruption of SETD3‐mediated histidine‐73 methylation by the BWCFF‐associated β‐actin G74S mutation
FEBS Letters, EarlyView.The β‐actin G74S mutation causes altered interaction of actin with SETD3, reducing histidine‐73 methylation efficiency and forming two distinct actin variants. The variable ratio of these variants across cell types and developmental stages contributes to tissue‐specific phenotypical changes. This imbalance may impair actin dynamics and mechanosensitive
Anja Marquardt +8 more
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Mean Curvature Type Flow with Perpendicular Neumann Boundary Condition inside a Convex Cone
Abstract and Applied Analysis, 2014 We investigate the evolution of hypersurfaces with perpendicular Neumann boundary condition under mean curvature type flow, where the boundary manifold is a convex cone.
Fangcheng Guo, Guanghan Li, Chuanxi Wu
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Mathematical and Computational Applications, 2019 We study a variational problem for hypersurfaces in the Euclidean space with an anisotropic surface energy. An anisotropic surface energy is the integral of an energy density that depends on the surface normal over the considered hypersurface, which was ...
Miyuki Koiso
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Uniqueness and Pseudolocality Theorems of the Mean Curvature Flow
, 2006 Mean curvature flow evolves isometrically immersed base manifolds $M$ in the direction of their mean curvatures in an ambient manifold $\bar{M}$. If the base manifold $M$ is compact, the short time existence and uniqueness of the mean curvature flow are ...
Chen, Bing-Long, Yin, Le
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Circulating histones as clinical biomarkers in critically ill conditions
FEBS Letters, EarlyView.Circulating histones are emerging as promising biomarkers in critical illness due to their diagnostic, prognostic, and therapeutic potential. Detection methods such as ELISA and mass spectrometry provide reliable approaches for quantifying histone levels in plasma samples.
José Luis García‐Gimenez +17 more
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The extension and convergence of mean curvature flow in higher codimension [PDF]
, 2011 In this paper, we first investigate the integral curvature condition to extend the mean curvature flow of submanifolds in a Riemannian manifold with codimension $d\geq1$, which generalizes the extension theorem for the mean curvature flow of ...
Liu, Kefeng +3 more
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