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.