Balls in Teichmüller space are not convex

by Prof. Kasra RAFI (Université de Toronto)

Monday Feb 6, 2017, 2:30 PM → 3:45 PM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

We prove that when 3g − 3 + p > 3, the Teichmüller space of the closed surface of genus g with p punctures contains balls which are not convex in the Teichmüller metric. We analyze the quadratic differential associated to a Teichmüller geodesic and, as a key step, show that the extremal length of a curve (as a function of time) can have a local maximum. This is a joint work with Maxime Fortier Bourque.