纸折叠、Riemann surfaces和伪Anosov序列的收敛性
Paper folding, Riemann surfaces, and convergence of pseudo-Anosov sequences
摘要：
给出了一种由沿边界具有无穷多个线段标识的欧氏多边形构造闭曲面的方法。商上的度量被识别。给出了一个充分条件，保证多边形上的欧氏结构在商曲面上导出唯一的共形结构，使其成为闭的黎曼曲面.在这种情况下，一个模的连续性均匀化坐标被发现，这只取决于几何形状的多边形和上的标识。给出了一类伪Anosov同胚的一致连续模的应用，证明了它们收敛于Riemann球面上的Teichmüller映射.
英文摘要：
A method is presented for constructing closed surfaces out of Euclidean polygons with infinitely many segment identifications along the boundary. The metric on the quotient is identified. A sufficient condition is presented which guarantees that the Euclidean structure on the polygons induces a unique conformal structure on the quotient surface, making it into a closed Riemann surface. In this case, a modulus of continuity for uniformizing coordinates is found which depends only on the geometry of the polygons and on the identifications. An application is presented in which a uniform modulus of continuity is obtained for a family of pseudo-Anosov homeomorphisms, making it possible to prove that they converge to a Teichmüller mapping on the Riemann sphere.
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