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

Abstract

We study two 2-dimensional Teichmüller spaces of surfaces with boundary and marked points, namely, the pentagon and the punctured triangle. We show that their geometry is quite different from Teichmüller 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.

Publication
Geometriae Dedicata, 197, pp. 193–227
Yudong Chen
Yudong Chen
Assistant Professor in Statistics

My research interests include changepoint detection, high-dimensional statistics, robust statistcs, online algorithms and machine learning.