Non-convex balls in the Teichmüller metric

Abstract

We prove that the Teichmüller space of surfaces of genus $\mathbf{g}$ with $\mathbf{p}$ punctures contains balls which are not convex in the Teichmüller metric whenever $3\mathbf{g}-3+\mathbf{p}>1$.

34 pages, 6 figures