论文标题
一个零lyapunov的指数$ 3 $表示Eierlegende Wollmilchsau
A Zero Lyapunov Exponent in Genus $3$ Implies the Eierlegende Wollmilchsau
论文作者
论文摘要
我们证明，eiergende wollmilchsau的闭合轨道是唯一的$ \ text {sl}（2，\ mathbb {r}）$ - 在其kontsevich-zorich Spectrum中具有零lyapunov exponent的属属的属于三属的轨道闭合。该结果恢复了贝恩布里奇·哈贝格·莫勒（Bainbridge-Habegger-Möller）和第一个命名作者在这个方向上恢复了以前的部分结果。主要的新贡献是对沿曲线模量空间边界的变性的Forni子空间的理解。这导致了一个简单的几何标准，该标准排除了Forni子空间的存在。另一个关键要素是解决HU工作和第三名作者的跳跃问题的解决方案。
We prove that the closed orbit of the Eierlegende Wollmilchsau is the only $\text{SL}(2,\mathbb{R})$-orbit closure in genus three with a zero Lyapunov exponent in its Kontsevich-Zorich spectrum. The result recovers previous partial results in this direction by Bainbridge-Habegger-Möller and the first named author. The main new contribution is an understanding of the Forni subspace along a degeneration toward the boundary of the moduli space of curves. This results in a simple geometric criterion that excludes the existence of a Forni subspace. Another key ingredient is the solution to the jump problem from the work of Hu and the third named author.
