论文标题
$ \ mathrm {so} _ {0}（2,3）$ - hitchin component的长度光谱紧凑
Length spectrum compactification of the $\mathrm{SO}_{0}(2,3)$-Hitchin component
论文作者
论文摘要
我们发现$ \ mathrm {so} _ {0}（2,3）$ - Hitchin组件的紧凑型通过研究在4-维伪二维伪造的唯一最大最大表面上的诱导度量的变性，以实现4-维伪造型 - hyperbolic Space $ \ Mathbb $ \ MathBb $ \ MathBb {在此过程中，我们建立了在riemann表面上由霍明型四分化差异引起的扁平指标空间的项目活动的地理电流的封闭。作为应用程序，我们描述了沿着四分位差异射线的Hitchin表示熵的行为。
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.
