Abstract

We prove that a generically regular semisimple Higgs bundle equipped with a nondegenerate symmetric pairing on any Riemann surface always has a harmonic metric compatible with the pairing. We also study the classification of such compatible harmonic metrics in the case where the Riemann surface is the complement of a finite set $D$ in a compact Riemann surface. In particular, we prove the uniqueness of a compatible harmonic metric if the Higgs bundle is wild and regular semisimple at each point of $D$.

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