The asymptotic behavior of the monodromy representation of the associated family of a compact CMC surface (Q2830646)

From the author's abstract: Constant mean curvature (CMC) surfaces in space forms can be described by their associated C*-family of flat \(\mathrm{SL}(2,\mathbb C)\)-connections \(\nabla\lambda\). In this paper, we consider the asymptotic behavior (for \(\lambda\to 0\)) of the gauge equivalence classes of \(\nabla\lambda\) for compact CMC surfaces of genus \(g\geq 2\). We prove (under the assumption of simple umbilics) that the asymptotic behavior of the traces of the monodromy representation of \(\nabla\lambda\) determines the conformal type as well as the Hopf differential locally in the Teichmüller space.