Ricci Yang-Mills flow on surfaces

We study the behavior of the Ricci Yang-Mills flow for U(1) bundles on surfaces. By exploiting a coupling of the Liouville and Yang-Mills energies we show that existence for the flow reduces to a bound on the isoperimetric constant or the L⁴ norm of the bundle curvature. We furthermore completely describe the behavior of long time solutions of this flow on surfaces. Finally, in Appendix A we classify all gradient solitons of this flow on surfaces.