Extremal mappings of tori, Teichmüller potentials and symmetric-space distance

Benson Farb, Eduard Looijenga

The symmetric space $X_n={\rm SL}(n,\Rb)/{\rm SO}(n)$ can be interpreted as the Teichmüller space of marked, unit volume, flat $n$-dimensional tori. It comes with a unique (up to s…