The Yang-Mills flow near the boundary of Teichmueller space

Details The Yang-Mills flow near the boundary of Teichmueller space The Yang-Mills flow near the boundary of Teichmueller space

1998-10-06

arxiv.org/abs/math/9810032v1

Mathematics

Differential Geometry

35 pages. Latex

Scientific paper

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 Teichm\"uller 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 Teichm\"uller space, and continuity of this extension is the main result of the paper.

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