全纯映射与全纯叠层的相切

A bound on the $L^2$-norm of a projective structure by the length of the bending lamination

One can associate to a complex projective structure on a surface holomorphic quadratic differential $Φ$ via the Schwarzian derivative and a bending lamination $λ$ via the Thurston parameterization. In this note we obtain upper bounds on the $L^2$-norm of $Φ$ in terms of the length of $λ$. The proof uses the theory of $W$-volume introduced by Krasnov-Schlenker.

Ergodic theorems for laminations and foliations: recent results and perspectives

This report discusses recent results as well as new perspectives in the ergodic theory for Riemann surface laminations, with an emphasis on singular holomorphic foliations by curves. The central notions of these developments are leafwise Poincaré metric, directed positive harmonic currents, multiplicative cocycles and Lyapunov exponents. We deal with various ergodic theorems for such laminations: Random and Operator Ergodic Theorems, (Geometric) Birkhoff Ergodic Theorems, Oseledec Multiplicative Ergodic Theorem and Unique Ergodicity Theorems. Applications of these theorems are also given. In p…

关于$\mathbb{CP}^2$中非平凡层的存在性

On the existence of non-trivial laminations in $\mathbb{CP}^2$

本文利用Donaldson构造的渐近全纯子流形证明了嵌入$\mathbb{CP}^2$中的非平凡Riemann曲面层的存在性.进一步，我们得到的层具有的性质，每个叶是一个全测地子流形的$\mathbb{CP}^2 $关于Fubini-Study度量。这可能是理解$\mathbb{CP}^2$中最小例外集存在性猜想的一个步骤。

曲面分支与孤立$ε$ -全纯

Surfaces branchées et soléno\"ıdes $ε$-holomorphes

证明了对每一个$ε>0$，在复射影平面上存在一个由$ε$ -全纯曲面构成的紧致层积，该层积极小，且具有双曲型全纯性.我们称$ε$ -全纯为${\bf C}P^2$中的一个实二维曲面$Σ$，使得$TΣ$和$iTΣ$之间的夹角被$ε$一致有界.当$ε$足够小时，这样的曲面特别是辛的。

全纯叶状结构与曲线的几何指标定理

Geometric index theorems for holomorphic foliations and curves

本文针对复曲面上的全纯叶状结构，引入相对指标并证明其和等于相交数，进而推导出两个接触公式，推广了 Plücker 公式且不依赖参考叶状结构。

黎曼曲面上叶状结构对的全纯实现

Holomorphic realizations of pairs of foliations on Riemann surfaces

将 Gardiner-Masur 定理推广到任意双曲黎曼曲面，证明填充叶状结构对可由全纯二次微分的水平与垂直叶状结构实现，并应用于渐近 Plateau 问题及映射类群。

扩张Thurston映射的完美拟合无限链

Infinite chains of perfect fits for expanding Thurston maps

该研究证明多项式配对中完美拟合无限链不存在的结论是全纯现象，构造了含周期临界轨道的组合扩张Thurston映射，其层叠结构存在无限多完美拟合无限链，且无法由扩张有理映射实现。