作为双曲曲面模的简单长度谱及长度恒等式的刚性

Rigidity of Polyhedral Surfaces

We study rigidity of polyhedral surfaces and the moduli space of polyhedral surfaces using variational principles. Curvature like quantities for polyhedral surfaces are introduced. Many of them are shown to determine the polyhedral metric up to isometry. The action functionals in the variational approaches are derived from the cosine law and the Lengendre transformation of them. These include energies used by Colin de Verdiere, Braegger, Rivin, Cohen-Kenyon-Propp, Leibon and Bobenko-Springborn for variational principles on triangulated surfaces. Our study is based on a set of identities satisf…

Rigidity of moduli spaces and algebro-geometric constructions

In this paper we propose two guiding principles that suggest a number of conjectures (some now proved) about various forms of rigidity for moduli spaces arising in algebraic geometry. Such conjectures have group-theoretic, topological and holomorphic aspects, and so they also provide motivation for natural problems in geometric group theory and topology.

Orthospectra of Geodesic Laminations and Dilogarithm Identities on Moduli Space

Given a measured lamination on a finite area hyperbolic surface we consider a natural measure Mon the real line obtained by taking the push-forward of the volume measure of the unit tangent bundle of the surface under an intersection function associated with the lamination. We show that the measure M gives summation identities for the Rogers dilogarithm function on the moduli space of a surface.

Margulis 多重宇宙：无穷小刚性、压力形式与凸性

Margulis Multiverse: Infinitesimal Rigidity, Pressure Form and Convexity

本文研究高维无尖点 Margulis 时空模空间，构造压力形式，借助带标记 Margulis 不变量谱的无穷小确定性证明其在恒定熵截面上诱导黎曼度量，并确立固定线性部分时这些截面的凸性。

覆盖构造的局部刚性与曲线模空间的Weil–Petersson子簇

Local rigidity of covering constructions and Weil--Petersson subvarieties of the moduli space of curves

本文证明了曲线模空间$\u039c_{g,n}$的Weil–Petersson全测地子簇及覆盖构造是局部刚性的，该结论由一类轨形映射的一般刚性结果推导得到。

Global rigidity of the period mapping

Let ${\mathcal M}_{g,n}$ denote the moduli space of smooth, genus $g\geq 1$ curves with $n\geq 0$ marked points. Let ${\mathcal A}_h$ denote the moduli space of $h$-dimensional, principally polarized abelian varieties. Let $g\geq 3$ and $h\leq g$. If $F:{\mathcal M}_{g,n}\to{\mathcal A}_h$ is a nonconstant holomorphic map then $h=g$ and $F$ is the classical period mapping, assigning to a Riemann surface $X$ its Jacobian.