Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations
Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations
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平均曲率流讲义：障碍和奇异扰动
DOI：
10.1007/978-88-7642-429-8
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发表时间：
2014
影响因子：
2
通讯作者：
F. Pasquarelli
中科院分区：
文献类型：
--
作者：
G. Bellettini;V. Beorchia;M. Paolini;F. Pasquarelli
从光滑边界的符号距离。平均曲率向量和第二基本形式。体积积分和周长的第一变分。平滑的平均曲率流。Huisken的单调性公式包容性原则。局部适定性：Evans-Spruck的方法。格雷森的例子德乔治的屏障。内外正则化。一个增肥的例子。Ilmanen的插入引理回避原则。障碍与广义演化的比较。障碍和水平集进化。抛物奇异摄动：形式匹配渐近性、收敛性与误差估计。
Signed distance from a smooth boundary.- Mean curvature vector and second fundamental form.- First variations of volume integrals and of the perimeter.- Smooth mean curvature flows.- Huisken's monotonicity formula.- Inclusion principle. Local well posedness: the approach of Evans-Spruck.- Grayson's example.- De Giorgi's barriers.- Inner and outer regularizations.- An example of fattening.- Ilmanen's interposition lemma.- The avoidance principle.- Comparison between barriers and a generalized evolution.- Barriers and level set evolution.- Parabolic singular perturbations: formal matched asymptotics, convergence and error estimate.