Non-convex balls in the Teichm\"uller metric
  We prove that the Teichm\"uller space of surfaces of genus $\mathbf{g}$ with $\mathbf{p}$ punctures contains balls which are not convex in the Teichm\"uller metric whenever $3\mathbf{g}-3+\mathbf{p} > 1$. 
Maxime Fortier Bourque and Kasra Rafi
math.GT