On cyclic Higgs bundles

Song Dai; Qiongling Li

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arXiv · 1710.10725

On cyclic Higgs bundles

Song Dai·Qiongling Li

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Abstract

In this paper, we derive a maximum principle for a type of elliptic systems and apply it to analyze the Hitchin equation for cyclic Higgs bundles. We show several domination results on the pullback metric of the (possibly branched) minimal immersion $f$ associated to cyclic Higgs bundles. Also, we obtain a lower and upper bound of the extrinsic curvature of the image of $f$. As an application, we give a complete picture for maximal $Sp(4,\mathbb{R})$-representations in the $2g-3$ Gothen components and the Hitchin components.

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BibTeX RIS

Song Dai, Qiongling Li. 2017-10-30. On cyclic Higgs bundles. https://arxiv.org/abs/1710.10725

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