论文标题
抗De保姆的凸壳上的弯曲层板。
Bending laminations on convex hulls of anti-de Sitter quasicircles
论文作者
论文摘要
令$λ_- $和$λ_+$为双曲线磁盘$ \ Mathbb H^2 $上的两个有界测量的层压板，它“强烈填充”（下文定义）。 我们认为沿$λ_-$和$λ_+$的左震被认为是来自通用TeichMüller空间$ \ Mathcal T $的地图，我们证明那些左地震的组成有一个固定点。 证明使用反DE保姆的几何形状。给定一个准对称的同构$ u：{\ mathbb rp}^1 \ to {\ mathbb rp}^1 $，其图中的convex hull的边界$ {\ mathbb rp}^1 \ mathb rp}^1 \ times {双曲平面的两个嵌入式副本，沿着测得的大地层压板褶褶。我们的主要结果是，可以以这种方式获得“强烈填充”的任何有限的测量层压。
Let $λ_-$ and $λ_+$ be two bounded measured laminations on the hyperbolic disk $\mathbb H^2$, which "strongly fill" (definition below). We consider the left earthquakes along $λ_-$ and $λ_+$, considered as maps from the universal Teichmüller space $\mathcal T$ to itself, and we prove that the composition of those left earthquakes has a fixed point. The proof uses anti-de Sitter geometry. Given a quasi-symmetric homeomorphism $u:{\mathbb RP}^1\to {\mathbb RP}^1$, the boundary of the convex hull in $AdS^3$ of its graph in ${\mathbb RP}^1\times{\mathbb RP}^1\simeq \partial AdS^3$ is the disjoint union of two embedded copies of the hyperbolic plane, pleated along measured geodesic laminations. Our main result is that any pair of bounded measured laminations that "strongly fill" can be obtained in this manner.
