论文标题
飞机中无限反距离圆形包装的刚度
Rigidity of infinite inversive distance circle packings in the plane
论文作者
论文摘要
2004年，Bowers-Stephenson [2]引入了反距离圆形包装，作为Thurston圆形包装的自然概括。他们进一步猜测了飞机中无限的反距离圆形包装的刚性。由Luo-Sun-Wu [22]在Luo的顶点缩放上的最近工作的动机，我们证明了Bower-Stephenson在六角形三角凝平面中对反式距离圆形包装的猜想。这将Rodin-Sullivan的著名结果[13]概括为六边形三角剖分平面中无限切向圆圈的刚性。关键工具包括通用加权delaunay倒数距离圆形包装的最大原理和六边形三角态平面中的反距离圆形包装的环形引理。
In 2004, Bowers-Stephenson [2] introduced the inversive distance circle packings as a natural generalization of Thurston's circle packings. They further conjectured the rigidity of infinite inversive distance circle packings in the plane. Motivated by the recent work of Luo-Sun-Wu [22] on Luo's vertex scaling, we prove Bower-Stephenson's conjecture for inversive distance circle packings in the hexagonal triangulated plane. This generalizes Rodin-Sullivan's famous result [13] on the rigidity of infinite tangential circle packings in the hexagonal triangulated plane. The key tools include a maximal principle for generic weighted Delaunay inversive distance circle packings and a ring lemma for the inversive distance circle packings in the hexagonal triangulated plane.
