Mathematical Research Letters

Volume 7, Issue 1, January 2000 pp. 133-146.

Harmonic Maps to Teichmüller Space

Authors: Georgios Daskalopoulos, Ludmil Katzarkov, and Richard Wentworth
Author institution: Brown University, and University of California Irvine

Summary: 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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