Length spectrum compactification of the SO₀(2,3)-Hitchin component

We find a compactification of the SO0(2, 3)-Hitchin compo-nent by studying the degeneration of the induced metric on the unique equivariant maximal surface in the 4-dimensional pseudo-hyperbolic space H2,2. In the process, we establish the closure in the space of projectivized geodesic currents of the space of flat metrics induced by holomorphic quartic differ-entials on a Riemann surface. As an application, we describe the behavior of the entropy of the induced metric along rays of quartic differentials.(c) 2023 Elsevier Inc. All rights reserved.