In particular, we construct mean curvature flow solutions, in the rotationally symmetric class, with the following precise asymptotics near the "vanishing" time T: (1) The highest curvature concentrates at the tip of the hypersurface (an umbilical point) and blows up at the rate (Tt)1. (2)...
内容提示: LECTURES ON MEAN CURVATURE FLOWROBERT HASLHOFERAbstract. A family of hypersurfaces evolves by mean curvatureflow if the velocity at each point is given by the mean curva-ture vector. Mean curvature flow is the most natural evolutionequation in extrinsic geometry, and has been extensively...
Mean Curvature Flow的应用 1.形状优化:Mean Curvature Flow可以通过控制曲面上每个点的平均曲率,逐渐使曲面变得更加平滑。这在形状优化问题中非常有用,例如在三维打印中生成平滑的曲面模型。 2.图像分析:Mean Curvature Flow也可以用于图像分割和边缘检测等图像处理任务。通过应用Mean Curvature Flow来平滑图像的边缘,可以...
a generic mean curvature flow has only spherical and cylindrical singularities. the implications of this conjecture on the partial regularity and well-posedness of mean curvature flow is an important field of research in itself. see sect. 1.2 for the state of the art on the precise understand...
Daniel Depner, Harald Garcke, and Yoshihito Kohsaka, Mean curvature flow with triple junctions in higher space dimensions, Arch. Ration. Mech. Anal. 211 (2014), no. 1, 301-334.Daniel Depner, Harald Garcke, and Yoshihito Kohsaka. Mean curvature flow with triple junctions in higher space ...
mean_curvature_flow -回复 什么是平均曲率流(mean curvature flow)? 平均曲率流(mean curvature flow)是一种数学模型,用于描述曲面随着时间的演化过程。它是在1982年由数学家Richard Hamilton首次提出的。在平均曲率流的模型中,曲面上的每一点的演化速度与其平均曲率成正比。换句话说,曲面上的每个点都会以一个与...
Brakke’s mean curvature flow was first introduced in 1978 as a mathematical model describing the motion of grain boundaries in an annealing pure metal. The grain boundaries move by the mean curvature flow while retaining singularities such as triple junction points. By using a notion of ...
Mean curvature flow is the negative gradient flow of volume, so any hypersurface flows through hypersurfaces in the direction of steepest descent for volume and eventually becomes extinct in finite time. Before it becomes extinct, topological changes can occur as it goes through singularities. If the...
In this paper, we study the complete bounded λλ-hypersurfaces in the weighted volume-preserving mean curvature flow. Firstly, we investigate the volume comparison theorem of complete bounded λλ-hypersurfaces with |A|≤α|A|≤α and get some applications of the volume comparison theorem. Second...
Singularity Mean curvature flow 1. Introduction We consider a family of hypersurfaces {Mtn⊂Rn+1} evolving by mean curvature flow (MCF), which makes it satisfy the equation (1.1)dXMdt⊥=HM.where XM is the position vector and HM is the mean curvature vector. For a rich family of initial...