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Progress toward classifying Teichmuller disks with completely degenerate Kontsevich-Zorich spectrum.

机译：用完全退化的Kontsevich-Zorich光谱对Teichmuller圆盘进行分类的进展。

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We present results toward resolving a question posed by Eskin-Kontsevich-Zorich and Forni-Matheus-Zorich. They asked for a classification of all SL₂(

R

)-invariant ergodic probability measures with completely degenerate Kontsevich-Zorich spectrum. Let

D g

(1) be the subset of the moduli space of Abelian differentials

M g

whose elements have period matrix derivative of rank one. There is an SL₂(

R

)-invariant ergodic probability measure ν with completely degenerate Kontsevich-Zorich spectrum, i.e. λ₁ = 1 > λ₂ = ··· = λ_g = 0, if and only if ν has support contained in

D g

(1). We approach this problem by studying Teichmüller disks contained in

D g

(1). We show that if (X, ω) generates a Teichmüller disk in

D g

(1), then (X, ω) is completely periodic. Furthermore, we show that there are no Teichmüller disks in

D g

(1), for g = 2, and the known example of a Teichmüller disk in

D 3

(1) is the only one. Finally, we present an idea that might be able to fully resolve the problem.

机译：我们为解决Eskin-Kontsevich-Zorich和Forni-Matheus-Zorich提出的问题提供了结果。他们要求对所有SL _{2 （ $R ）不变的遍历概率度量进行分类，并使用完全退化的Kontsevich-佐里奇光谱。设 D g （1）是阿贝尔模数空间的子集 M g 的微分，其元素具有第一阶的周期矩阵导数。存在具有完全退化的Kontsevich-Zorich光谱的SL$ _{2 （ $R ）不变的遍历概率测度ν，即λ$ _{1 = 1>λ_{2 =···= λ_{g = 0，当且仅当ν在 $D g （1）中包含支持。我们通过研究 D g （1）中包含的Teichmüller磁盘来解决此问题。。我们证明如果（ X ，ω）在 D g 中生成Teichmüller磁盘（1），则（ X ，ω）是完全周期性的。此外，我们证明 D g （1中没有Teichmüller磁盘）， g = 2，以及 D 3 （1）是唯一的一个。最后，我们提出一个可能完全解决问题的想法。$}}}}}

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作者
Aulicino, David.;
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作者单位

University of Maryland, College Park.;

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授予单位 University of Maryland, College Park.;
学科 Mathematics.
学位 Ph.D.
年度 2012
页码 90 p.
总页数 90
原文格式 PDF
正文语种 eng
中图分类
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1. Teichmuller discs with completely degenerate Kontsevich-Zorich spectrum [J] . Aulicino David Commentarii Mathematici Helvetici . 2015,第3期

机译：具有完全退化的Kontsevich-Zorich光谱的Teichmuller光盘
2. Affine invariant submanifolds with completely degenerate Kontsevich-Zorich spectrum [J] . Aulicino David Ergodic Theory and Dynamical Systems . 2018,第Pta1期

机译：带有完全退化的kontsevich-zorich光谱的仿射不变子植物
3. Deviations de moyennes ergodiques, flats de Teichmuller et cocycle de Kontsevich-Zorich [J] . Raphael Krikorian Asterisque . 2005,第299期

机译：遍历均值，Teichmuller平底鞋和Kontsevich-Zorich摩托车的偏差
4. High efficiency, wide range and completely transparent wavelength conversion method using replicas generated by dual pump nearly-degenerated four-wave mixing in a Mach-Zehnder interferometer SOA [C] . K. Otsubo, S. Tanaka, S. Tomabechi, Optical Fiber Communication Conference . 2006

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5. Teichmuller Space of a Once Punctured Disk: Complex Coordinates on the Space of Abelian Differentials and the Takhtajan-Zograf Metric. [D] . Song, Ki Woo. 2012

机译：曾经被穿刺过的磁盘的Teichmuller空间：阿贝尔微分和Takhtajan-Zograf度量空间上的复数坐标。
6. Expression of metalloproteinases and their inhibitors in degenerated andextruded intervertebral disks in chondrodystrophic dogs [O] . Hirokazu ISHINO, Iwao SAKONJU 2021

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7. An example of a Teichmuller disk in genus 4 with degenerate Kontsevich-Zorich spectrum [O] . Forni, Giovanni, Matheus, Carlos 2008

机译：具有退化的4类Teichmuller盘的一个例子 Kontsevich-Zorich谱

Progress toward classifying Teichmuller disks with completely degenerate Kontsevich-Zorich spectrum.

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