Corona limits of tilings: Periodic case
Corona limits of tilings: Periodic case
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瓷砖的电晕极限：周期性情况
DOI：
10.1007/s00454-018-0033-x
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发表时间：
2019
影响因子：
0.8
通讯作者：
H Kaneko
中科院分区：
文献类型：
--
作者：
S Akiyama;J Caalim;K Imai;H Kaneko
我们研究了瓷砖连续冠状的极限形状，它模拟了晶体的生长。我们定义了基本术语，讨论了电晕极限的存在唯一性，并证明了电晕极限完全由方向速度来刻画。作为应用，我们给出了周期瓦片的电晕极限是中心对称凸多面体的另一个证明[参见朱拉夫列夫(St Petersbg Math J 13(2)：201-220,2002)和Maleev和Shutov(分区、填充和图的逐层增长模型，Tranzit-X，Vladimir，2011)]。
We study the limit shape of successive coronas of a tiling, which models the growth of crystals. We define basic terminologies and discuss the existence and uniqueness of corona limits, and then prove that corona limits are completely characterized by directional speeds. As an application, we give another proof that the corona limit of a periodic tiling is a centrally symmetric convex polyhedron [see Zhuravlev (St Petersbg Math J 13(2):201–220, 2002) and Maleev and Shutov (Layer-by-layer growth model for partitions, packings, and graphs, Tranzit-X, Vladimir, 2011)].