Regularity of Harmonic Maps from Riemann Surfaces to the Weil-Petersson Completion of Teichmueller Space

R. Wentworth

The main result states that the image of an energy minimizing map from a two dimensional domain to the metric completion of Teichmueller space with the Weil-Petersson metric lies in a single smooth stratum of the completion. Combined with previous work, this gives a criterion for the existence of equivariant harmonic maps from finite volume Riemann surfaces to Teichmueller space.