Quasi-Fuchsian flows and the coupled vortex equations
Dynamical Systems
2026-02-05 v3 Analysis of PDEs
Differential Geometry
Abstract
We provide an alternative construction of the quasi-Fuchsian flows introduced by Ghys in \cite{Ghys-92}. Our approach is based on the coupled vortex equations that allows to see these flows as thermostats on the unit tangent bundle of the Blaschke metric uniquely determined by a conformal class and a holomorphic quadratic differential. We also give formulas for the marked length spectrum of a quasi-Fuchsian flow in the thermostat parametrization.
Keywords
Cite
@article{arxiv.2501.10591,
title = {Quasi-Fuchsian flows and the coupled vortex equations},
author = {Mihajlo Cekić and Gabriel P. Paternain},
journal= {arXiv preprint arXiv:2501.10591},
year = {2026}
}
Comments
Minor revision, this version to appear in Bulletin LMS