Harmonic metrics of generically regular nilpotent Higgs bundles over non-compact surfaces

Song Dai, Qiongling Li

A rank $n$ Higgs bundle $(E,\hat{I}¸)$ is called generically regular nilpotent if $\hat{I}{¸}^n=0$ but $\hat{I}{¸}^{n-1}\ne 0$. We show that for a generically regular nilpotent Higgs bundle, if it admi…