Motion by curvature of planar networks II
Motion by curvature of planar networks II
复制标题
平面网络曲率运动 II
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
M. Novaga
中科院分区：
文献类型：
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作者：
A. Magni;C. Mantegazza;M. Novaga
我们证明了由三条曲线组成的嵌入平面网络的曲率流是光滑的，直到这三条曲线的长度远离零为止。如果所有时间都是这种情况，则演化始终存在，并且网络收敛到三个端点之间的Steiner最小连接。
We prove that the curvature flow of an embedded planar network of three curves connected through a triple junction, with fixed endpoints on the boundary of a given strictly convex domain, exists smooth until the lengths of the three curves stay far from zero. If this is the case for all times, then the evolution exists for all times and the network converges to the Steiner minimal connection between the three endpoints.