A criterion for density of the isoperiodic leaves in rank 1 affine invariant suborbifolds

Isoperiodic dynamics in rank 1 affine invariant orbifolds

Let M be a rank 1 affine invariant orbifold in a stratum of the moduli space of flat surfaces. We show that the leaves of the M-isoperiodic foliation are either all closed or all dense. In the second case, we establish ergodicity of the foliation with respect to the affine measure on M.

同周期叶状结构的 stratum $Ω\mathcal{M}_1(1,1,-2)$

Isoperiodic foliation of the stratum $Ω\mathcal{M}_1(1,1,-2)$

本文研究了 stratum $Ω\mathcal{M}_1(1,1,-2)$ 的同周期叶状结构，证明每个叶为无限亏格表面并支持奇异欧几里得结构，同时探讨了其 Veech 群和大规模共形几何。

一个转移原理：从周期到等周期叶状结构

A transfer principle: from periods to isoperiodic foliations

本研究分类了Hodge丛上等周期叶状结构的叶闭包并证明其遍历性，借助模空间Torelli覆叠上周期映射纤维的连通性推导结果，还得到椭圆曲线原始分支覆叠Hurwitz空间的拓扑推论，同时发展了增广Torelli空间理论。