Complete harmonic metrics and subharmonic functions on the unit disc

Let $X$ be a Riemann surface with canonical bundle $K_X$ and holomorphic tangent bundle $T_X=K_X^{-1}$. For each integer $r\geq 2$, each $q\in H^0(K_X^r)$, and each choice of a square root of $K_X$, we obtain a cyclic Higgs bundle. A diagonal harmonic metric $h=(h_1,\ldots,h_r)$ induces Hermitian me