Non-maximal Anosov Representations from Surface Groups to $\mathrm{SO}_0(2,3)$

We prove the representation given by a stable $\alpha_1$-cyclic parabolic $\mathrm{SO}_0(2,3)$-Higgs bundle through the non-Abelian Hodge correspondence is ${\alpha_2}$-almost dominated. This is a generalization of Filip’s result on weight $3$ variation of Hodge structures and answers a question asked by Collier, Tholozan and Toulisse.

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