Harmonic Maps to Teichmüller Space

We give sufficient conditions for the existence of equivariant harmonic maps from the universal cover of a Riemann surface $B$ to the Teichmüller space of a genus $g\geq 2$ surface $\Sigma$. The condition is in terms of the representation of the fundamental group of $B$ to the mapping class group of $\Sigma$. The metric on Teichmüller space is chosen to be the Kähler hyperbolic metric. Examples of such representations arise from symplectic Lefschetz fibrations.

Full Text (PDF format)

Published 1 January 2000