Non-uniqueness of minimal surfaces in a product of closed Riemann surfaces (Q2125152)

Let \(\sum_g\) be a surface of genus \(g\geq 2\), and let \(T_g\) be the Teichmüller space of marked complex structures on \(\sum_g\). In this work the author shows that for this \(g\), there exists a Fuchsian representation denoted by \(\rho:\pi_1(\sum_g)\to \Pi_{i=1}^3 \mathrm{PSL}(2, \mathbb{R}) \) such that the energy functional \(E\rho:T_g\to(0,\infty)\), which is given as the sum of energies of the corresponding harmonic diffeomorphisms, has at least two stationary points.