Toy Teichmüller spaces of real dimension 2: the pentagon and the punctured triangle

• DOI: 10.1007/s10711-018-0325-6
• Publication Date: 2018-02-02T12:39:07Z
• Authors: Yudong Chen; Roman Chernov; Marco Flores; Maxime Fortier Bo...; Seewoo Lee; Bowen Yang
• Keywords: Pentagon

We study two $2$-dimensional Teichm��ller spaces of surfaces with boundary and marked points, namely, the pentagon and the punctured triangle. We show that their geometry is quite different from Teichm��ller spaces of closed surfaces. Indeed, both spaces are exhausted by regular convex geodesic polygons with a fixed number of sides, and their geodesics diverge at most linearly.<br/>35 pages, 18 figures<br/>