On the Classification of Networks Self–Similarly Moving by Curvature
On the Classification of Networks Self–Similarly Moving by Curvature
复制标题
论曲率自相似运动网络的分类
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
C. Mantegazza
中科院分区：
文献类型：
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作者：
P. Baldi;E. Haus;C. Mantegazza
摘要本文概述了平面上至多有两个三结点的网络的分类，这些网络具有在曲率运动下自相似收缩的性质。在[7，9，20]的贡献之后，这样的分类在[4]的最近工作中完成（另见[3]），证明了没有自收缩网络同胚于希腊字母“theta”（一个双胞）嵌入平面中，两个三角形连接的角度为120度。我们提出的主要几何思想背后的工作[4]。我们还简要介绍了我们的工作进展中的高维情况下的网络的表面在R3。
Abstract We give an overview of the classification of networks in the plane with at most two triple junctions with the property that under the motion by curvature they are self-similarly shrinking. After the contributions in [7, 9, 20], such a classification was completed in the recent work in [4] (see also [3]), proving that there are no self-shrinking networks homeomorphic to the Greek “theta” letter (a double cell) embedded in the plane with two triple junctions with angles of 120 degrees. We present the main geometric ideas behind the work [4]. We also briefly introduce our work in progress in the higher-dimensional case of networks of surfaces in R3.