The Yang-Mills flow near the boundary of Teichmueller space

Abstract

We study the behavior of the Yang-Mills flow for unitary connections on compact and non-compact oriented surfaces with varying metrics. The flow can be used to define a one dimensional foliation on the space of SU(2) representations of a once punctured surface. This foliation universalizes over Teichmüller space and is equivariant with respect to the action of the mapping class group. It is shown how to extend the foliation as a singular foliation over the Strebel boundary of Teichmüller space, and continuity of this extension is the main result of the paper.