The Yang-Mills flow near the boundary of Teichmüller 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 Teichmuller 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 augmented boundary of Teichmuller space obtained by adding nodal Riemann surfaces. Continuity of this extension is the main result of the paper.