Non–existence of theta–shaped self–similarly shrinking networks moving by curvature
Non–existence of theta–shaped self–similarly shrinking networks moving by curvature
复制标题
不存在按曲率移动的θ形自相似收缩网络
DOI：
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发表时间：
2016
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
本文证明了在具有120度角的两个三结点的平面上，不存在与希腊“theta”字母(双胞格)同胚的网络，使得它们在曲率运动下自相似收缩。这一事实完成了对平面上至多有两个三重结的自相似收缩网络的分类，见[5，10，25，2]。
ABSTRACT We prove that there are no networks homeomorphic to the Greek “Theta” letter (a double cell) embedded in the plane with two triple junctions with angles of 120 degrees, such that under the motion by curvature they are self–similarly shrinking. This fact completes the classification of the self–similarly shrinking networks in the plane with at most two triple junctions, see [5, 10, 25, 2].