Mean Curvature Flow的数学原理 Mean CurvatureFlow是基于曲面的法向方向和曲率来推导的。假设有一个参数化的曲面S(u,v),其法向量为N(u,v)。曲面上每一点的曲率可以通过曲面的二阶导数来计算得到。在曲面上的某一点P,曲率是由法向方向上的两个主方向上的曲率构成的。曲率的方向决定了曲面的曲率流。 Mean Curva...
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...
We prove long-time existence and convergence results for spacelike solutions to mean curvature flow in the pseudo-Euclidean space \\(\\mathbb {R}^{n,m}\\), which are entire or defined on bounded domains and satisfying Neumann or Dirichlet boundary conditions. As an application, we prove ...
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 stud-ied...
... ) the mean curvature flow 平均曲率流 ) mean curvature flow 平均曲率流 ) contra-harmonic mean 反调和平均数 ... www.dictall.com|基于3个网页 例句 释义: 全部,平均曲率流 更多例句筛选 1. The paper presents a smoothing algorithm based on the main direction combined with the mean curvature...
. unlike the traditional heat equation, mean curvature flow is nonlinear. as a result, the mean curvature flow starting at a closed surface \(m\subset \mathbb{r}^{3}\) is guaranteed to become singular in finite time. there are numerous possible singularities and, in general, they can ...
mean-curvatureflow under the restriction that the networks are Voronoi diagrams for a set of points.For such evolution we prove a rigorous universal upper bound on the coarsening rate.The rate agrees with the rate predicted for the evolution by mean-curvature flow of thegeneral grain boundary ...
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...
The mean curvature flow is an evolution process under which a submanifold deforms in the direction of its mean curvature vector. The hypersurface case has been much studied since the eighties. Recently, several theorems on regularity, global existence and convergence of the flow in various ambient...
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 ...