Mathematical Research Letters

Volume 7 (2000)

Number 1

Harmonic Maps to Teichmüller Space

Pages: 133 – 146



Georgios Daskalopoulos

Ludmil Katzarkov

Richard Wentworth


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.

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