A Zero Lyapunov Exponent in Genus $3$ Implies the Eierlegende Wollmilchsau

David Aulicino, Frederik Benirschke, Chaya Norton

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-Zo…