拟代数和Z^γ-圈模式的刚性
Rigidity of quasicrystallic and Z^γ-circle patterns
摘要：
在给定组合数学和某些边界条件的情况下，证明了Bobenko和Agafonov研究的正交Z^γ-圆模式的唯一性。此外，我们还研究了平面上的（无限）菱形嵌入，它们是拟菱形的，即它们只有200个不同的边方向。对菱形的顶点进行双色，并在其中一种颜色的顶点上添加圆心和半径等于边长的圆，这就产生了等径准菱形圆图案。我们证明了一个大类的这样的圆形图案，覆盖整个平面，他们是唯一确定的仿射变换的组合和相交角。结合这两个结果，我们得到了大类拟对称Z^γ-圈模式的刚性.
英文摘要：
The uniqueness of the orthogonal Z^γ-circle patterns as studied by Bobenko and Agafonov is shown, given the combinatorics and some boundary conditions. Furthermore we study (infinite) rhombic embeddings in the plane which are quasicrystallic, that is they have only finitely many different edge directions. Bicoloring the vertices of the rhombi and adding circles with centers at vertices of one of the colors and radius equal to the edge length leads to isoradial quasicrystallic circle patterns. We prove for a large class of such circle patterns which cover the whole plane that they are uniquely determined up to affine transformations by the combinatorics and the intersection angles. Combining these two results, we obtain the rigidity of large classes of quasicrystallic Z^γ-circle patterns.
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