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Bers’ simultaneous uniformization and the intersection of Poincaré holonomy varieties Bers的同时一致化与Poincaréholonomy变种的交集
IF 2.2 1区 数学 Q1 MATHEMATICS
Geometric and Functional Analysis
Pub Date : 2023-10-31 DOI: 10.1007/s00039-023-00653-8
Shinpei Baba

We consider the space of ordered pairs of distinct ({mathbb{C}{mathrm{P}}}^{1})-structures on Riemann surfaces (of any orientations) which have identical holonomy, so that the quasi-Fuchsian space is identified with a connected component of this space. This space holomorphically maps to the product of the Teichmüller spaces minus its diagonal.

In this paper, we prove that this mapping is a complete local branched covering map. As a corollary, we reprove Bers’ simultaneous uniformization theorem without any quasi-conformal deformation theory. Our main theorem is that the intersection of arbitrary two Poincaré holonomy varieties ((operatorname{SL}_{2}mathbb{C})-opers) is a non-empty discrete set, which is closely related to the mapping.

我们考虑具有相同全息性的（任何方向的）黎曼曲面上的不同结构的有序对的空间，使得准Fuchsian空间被识别为该空间的连通分量。这个空间全纯映射到Teichmüller空间减去其对角线的乘积。本文证明了该映射是一个完全的局部分支覆盖映射。作为推论，我们在没有任何拟共形变形理论的情况下，重新提出了Bers的同时一致化定理。我们的主要定理是任意两个Poincaréholonomy变种（（ operatorname{SL}_{2} mathbb｛C｝）-运算器）是一个非空离散集，它与映射密切相关。
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引用次数: 0
Contribution of n-cylinder square-tiled surfaces to Masur–Veech volume of $mathcal{H}(2g-2)$ n柱方形瓷砖表面对Masur–Veech体积的贡献$mathcal｛H｝（2g-2）$
IF 2.2 1区 数学 Q1 MATHEMATICS
Geometric and Functional Analysis
Pub Date : 2023-10-12 DOI: 10.1007/s00039-023-00652-9
Ivan Yakovlev

We find the generating function for the contributions of n-cylinder square-tiled surfaces to the Masur–Veech volume of (mathcal{H}(2g-2)). It is a bivariate generalization of the generating function for the total volumes obtained by Sauvaget via intersection theory. Our approach is, however, purely combinatorial. It relies on the study of counting functions for certain families of metric ribbon graphs. Their top-degree terms are polynomials, whose (normalized) coefficients are cardinalities of certain families of metric plane trees. These polynomials are analogues of Kontsevich polynomials that appear as part of his proof of Witten’s conjecture.

我们找到了n-圆柱体正方形瓷砖表面对（mathcal｛H｝（2g-2））的Masur–Veech体积的贡献的生成函数。它是Sauvaget通过交集理论获得的总体积的生成函数的二元推广。然而，我们的方法纯粹是组合的。它依赖于对某些度量带状图族的计数函数的研究。它们的最高阶项是多项式，其（归一化）系数是度量平面树的某些族的基数。这些多项式是Kontsevich多项式的类似物，出现在他对Witten猜想的证明中。
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引用次数: 0
Concentration of invariant means and dynamics of chain stabilizers in continuous geometries 连续几何中不变均值的集中与链稳定器的动力学
IF 2.2 1区 数学 Q1 MATHEMATICS
Geometric and Functional Analysis
Pub Date : 2023-10-12 DOI: 10.1007/s00039-023-00651-w
Friedrich Martin Schneider

We prove a concentration inequality for invariant means on topological groups, namely for such adapted to a chain of amenable topological subgroups. The result is based on an application of Azuma’s martingale inequality and provides a method for establishing extreme amenability. Building on this technique, we exhibit new examples of extremely amenable groups arising from von Neumann’s continuous geometries. Along the way, we also answer a question by Pestov on dynamical concentration in direct products of amenable topological groups.

我们证明了拓扑群上不变均值的一个集中不等式，也就是说，它适用于一个可服从的拓扑子群链。该结果基于Azuma的鞅不等式的一个应用，并提供了一种建立极端可适性的方法。在这项技术的基础上，我们展示了冯·诺依曼连续几何中产生的极易服从群的新例子。在此过程中，我们还回答了Pestov关于服从拓扑群的直积中的动力学集中的问题。
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引用次数: 1
Isometric group actions with vanishing rate of escape on $$textrm{CAT}(0)$$ spaces $$textrm{CAT}(0)$$空间上具有逃逸消失率的等长群作用
1区 数学 Q1 MATHEMATICS
Geometric and Functional Analysis
Pub Date : 2023-01-24 DOI: 10.1007/s00039-023-00628-9
Hiroyasu Izeki
Let $Gamma$ be a finitely generated group equipped with a symmetric and nondegenerate probability measure $mu$ with finite second moment, and $Y$ a CAT(0) space which is either proper or of finite telescopic dimension. We show that if an isometric action of $Gamma$ on $Y$ has vanishing rate of escape with respect to $mu$ and does not fix a point in the boundary at infinity of $Y$, then there exists a flat subspace in $Y$ which is left invariant under the action of $Gamma$. In the proof of this result, an equivariant $mu$-harmonic map from $Gamma$ into $Y$ plays an important role.
设$Gamma$是一个有限生成的群，具有有限第二矩的对称非退化概率测度$mu$, $Y$是一个固有维数或有限伸缩维数的CAT(0)空间。我们证明了如果$Gamma$在$Y$上的等距作用相对于$mu$具有逃逸消失率，并且在$Y$的无穷远处边界上不固定一个点，则在$Y$上存在一个平坦子空间，该子空间在$Gamma$作用下保持不变。在证明这一结果的过程中，一个从$Gamma$到$Y$的等变$mu$ -调和映射起了重要的作用。
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引用次数: 1
Tori Approximation of Families of Diagonally Invariant Measures 对角不变测度族的Tori逼近
IF 2.2 1区 数学 Q1 MATHEMATICS
Geometric and Functional Analysis
Pub Date : 2023-01-02 DOI: 10.1007/s00039-023-00646-7
O. Solan, Y. Yifrach
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引用次数: 0
Publisher Correction to: The generalized doubling method: local theory 出版商更正：广义加倍方法：局部理论
IF 2.2 1区 数学 Q1 MATHEMATICS
Geometric and Functional Analysis
Pub Date : 2022-11-29 DOI: 10.1007/s00039-022-00622-7
Yuanqing Cai, S. Friedberg, Eyal Kaplan
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引用次数: 0
The Spectrum of Schrödinger Operators with Randomly Perturbed Ergodic Potentials 具有随机摄动遍历势的Schrödinger算子的谱
IF 2.2 1区 数学 Q1 MATHEMATICS
Geometric and Functional Analysis
Pub Date : 2022-11-03 DOI: 10.1007/s00039-023-00632-z
A. Avila, D. Damanik, A. Gorodetski
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引用次数: 2
Diameter estimates for long-time solutions of the Kähler–Ricci flow Kähler–Ricci流长期解的直径估计
IF 2.2 1区 数学 Q1 MATHEMATICS
Geometric and Functional Analysis
Pub Date : 2022-10-22 DOI: 10.1007/s00039-022-00620-9
Wangjian Jian, Jian Song
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引用次数: 3
The generalized doubling method: local theory 广义加倍方法：局部理论
IF 2.2 1区 数学 Q1 MATHEMATICS
Geometric and Functional Analysis
Pub Date : 2022-09-29 DOI: 10.1007/s00039-022-00609-4
Yuanqing Cai, S. Friedberg, Eyal Kaplan
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引用次数: 6
An exotic II1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$_1$$end{document} factor without property Gamma An exotic II1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$_1$$end{document} factor without property Gamma
IF 2.2 1区 数学 Q1 MATHEMATICS
Geometric and Functional Analysis
Pub Date : 2022-09-21 DOI: 10.1007/s00039-023-00649-4
I. Chifan, A. Ioana, Srivatsav Kunnawalkam Elayavalli
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引用次数: 1
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