Quasi-Fuchsian flows and the coupled vortex equations
Vortrag von Dr. Mihajlo Cekić
Datum: 12.03.25 Zeit: 13.30 - 14.30 Raum: ETH HG G 19.1
In 1992, Ghys introduced a remarkable class of flows called quasi-Fuchsian flows. Namely, for a pair of metrics g_1 and g_2 of constant curvature -1 on a closed surface M, corresponding to points in Teichmueller space [g_1] and [g_2], respectively, he constructed an Anosov flow \phi_{[g_1], [g_2]} on the bundle of positive half-lines over M, whose weak stable and unstable foliations are smoothly conjugated to that of the geodesic flows of g_1 and g_2, respectively. In fact, in 1993 Ghys also showed that any Anosov flow on a 3-manifold with smooth weak stable/unstable bundles is smoothly conjugate to a quasi-Fuchsian flow or a suspension of a diffeomorphism of the 2-torus. In this talk, I will give an alternative 'PDE theoretic' description of quasi-Fuchsian flows as certain thermostat flows on the unit tangent bundle of the Blaschke metric uniquely determined by a conformal class on M and a holomorphic quadratic differential, satisfying `coupled vortex equations'. Joint work with Gabriel Paternain.