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arXiv · 2010.03499

Length spectrum compactification of the $\mathrm{SO}_{0}(2,3)$-Hitchin component

Charles Ouyang·Andrea Tamburelli
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Abstract

We find a compactification of the $\mathrm{SO}_{0}(2,3)$-Hitchin component by studying the degeneration of the induced metric on the unique equivariant maximal surface in the 4-dimensional pseudo-hyperbolic space $\mathbb{H}^{2,2}$. In the process, we establish the closure in the space of projectivized geodesic currents of the space of flat metrics induced by holomorphic quartic differentials on a Riemann surface. As an application, we describe the behavior of the entropy of Hitchin representations along rays of quartic differentials.

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Charles Ouyang, Andrea Tamburelli. 2020-10-07. Length spectrum compactification of the $\mathrm{SO}_{0}(2,3)$-Hitchin component. https://arxiv.org/abs/2010.03499

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