Length spectrum compactification of the ${\mathrm{SO}}_0(2,3)$-Hitchin component

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.

34 pages, comments welcome

References in corpus (4)

• G2 geometry and integrable systems
• Survey on Affine Spheres
• Length spectral rigidity of non-positively curved surfaces
• A structure theorem for geodesic currents and length spectrum compactifications

Cited by in corpus (1)

• Boundary of the Gothen components