Geometric and Functional Analysis最新文献

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A Sharp Square Function Estimate for the Moment Curve in $mathbb{R}^{n}$ $mathbb{R}^{n}$中矩曲线的锐平方函数估计

IF 2.2 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis

Pub Date : 2026-03-11 DOI: 10.1007/s00039-026-00736-2

Larry Guth, Dominique Maldague

引用次数: 0

Contact Big Fiber Theorems 联系大纤维定理

IF 2.2 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis

Pub Date : 2026-02-25 DOI: 10.1007/s00039-026-00734-4

Yuhan Sun, Igor Uljarević, Umut Varolgunes

We prove contact big fiber theorems, analogous to the symplectic big fiber theorem by Entov and Polterovich, using symplectic cohomology with support. Unlike in the symplectic case, the validity of the statements requires conditions on the closed contact manifold. One such condition is to admit a Liouville filling with non-zero symplectic cohomology. In the case of Boothby-Wang contact manifolds, we prove the result under the condition that the Euler class of the circle bundle, which is the negative of an integral lift of the symplectic class, is not an invertible element in the quantum cohomology of the base symplectic manifold. As applications, we obtain new examples of rigidity of intersections in contact manifolds and also of contact non-squeezing.

利用有支持的辛上同调定理，证明了类似于Entov和Polterovich的辛大纤维定理的接触大纤维定理。与辛情况不同，这些表述的有效性需要在闭合接触流形上的条件。一个这样的条件是允许一个具有非零辛上同的Liouville填充。在Boothby-Wang接触流形的情况下，我们证明了圆束的欧拉类在基辛流形的量子上同调中不是可逆元的条件下的结果，该欧拉类是辛类的一个积分升的负数。作为应用，我们得到了接触流形中相交刚度和接触非挤压的新实例。

引用次数: 0

Lossless Strichartz and Spectral Projection Estimates on Unbounded Manifolds 无界流形的无损Strichartz和谱投影估计

IF 2.2 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis

Pub Date : 2026-02-18 DOI: 10.1007/s00039-026-00732-6

Xiaoqi Huang, Christopher D. Sogge, Zhongkai Tao, Zhexing Zhang

引用次数: 0

Strong Asymptotic Freeness of Haar Unitaries in Quasi-Exponential Dimensional Representations 准指数维表示中Haar酉的强渐近自由性

IF 2.2 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis

Pub Date : 2026-02-18 DOI: 10.1007/s00039-026-00730-8

Michael Magee, Mikael de la Salle

We prove almost sure strong asymptotic freeness of i.i.d. random unitaries with the following law: sample a Haar unitary matrix of dimension

$n$

n and then send this unitary into an irreducible representation of

$mathrm{U}(n)$

U ( n ) . The strong convergence holds as long as the irreducible representation arises from a pair of partitions of total size at most

$n^{frac{1}{42}-varepsilon }$

n 1 42 − ε and is uniform in this regime. Previously this was known for partitions of total size up to

$asymp log n/log log n$

≍ log n / log log n by a result of Bordenave and Collins.

我们用以下定律证明了i.i.d随机酉的几乎肯定的强渐近自由性：抽样一个维数为$n$ n的Haar酉矩阵，然后把这个酉变换成一个不可约的$mathrm{U}(n)$ U (n)表示。只要不可约表示产生于总大小不超过$n^{frac{1}{42}-varepsilon }$ n 1 42−ε的一对分区，并且在此区域内是一致的，则强收敛性成立。以前，Bordenave和Collins的结果表明，总大小可达$asymp log n/log log n$ / log n / log log n的分区是已知的。

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引用次数: 0

Deformations of $mathbb{Z}_{2}$-Harmonic Spinors on 3-Manifolds 3-流形上$mathbb{Z}_{2}$-谐旋量的变形

IF 2.2 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis

Pub Date : 2026-02-16 DOI: 10.1007/s00039-026-00729-1

Gregory J. Parker

引用次数: 0

Complete Classification of the Dehn Functions of Bestvina–Brady Groups Bestvina-Brady群Dehn函数的完全分类

IF 2.2 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis

Pub Date : 2026-02-02 DOI: 10.1007/s00039-026-00731-7

Yu-Chan Chang, Jerónimo García-Mejía, Matteo Migliorini

We prove that the Dehn function of every finitely presented Bestvina–Brady group grows as a linear, quadratic, cubic, or quartic polynomial. In fact, we provide explicit criteria on the defining graph to determine the degree of this polynomial. As a consequence, we identify an obstruction that prevents certain Bestvina–Brady groups from admitting a CAT(0) structure.

我们证明了每一个有限呈现的Bestvina-Brady群的Dehn函数都是线性、二次、三次或四次多项式。事实上，我们在定义图上提供了明确的准则来确定这个多项式的度。因此，我们确定了阻止某些Bestvina-Brady组承认CAT(0)结构的障碍。

引用次数: 0

Quadratic Forms in 8 Prime Variables 8素数变量的二次型

IF 2.2 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis

Pub Date : 2025-12-05 DOI: 10.1007/s00039-025-00727-9

Ben Green

We give an asymptotic for the number of prime solutions to

$Q(x_{1},dots , x_{8}) = N$

Q ( x 1 , … , x 8 ) = N , subject to a mild non-degeneracy condition on the homogeneous quadratic form

$Q$

Q . The argument initially proceeds via the circle method, but this does not suffice by itself. To obtain a nontrivial bound on certain averages of exponential sums, we interpret these sums as matrix coefficients for the Weil representation of the symplectic group

$operatorname {Sp}_{8}(mathbf{Z}/qmathbf{Z})$

Sp 8 ( Z / q Z ) . Averages of such matrix coefficients are then bounded using an amplification argument and a convergence result for convolutions of measures, which reduces matters to understanding the action of certain 12-dimensional subgroups in the Weil representation. Sufficient understanding can be gained by using the basic represention theory of

$operatorname {SL}_{2}(k)$

SL 2 ( k ) ,

$k$

k a finite field.

给出了$Q(x_{1},dots, x_{8}) = N$ Q(x 1，…，x 8) = N在齐次二次形式$Q$ Q上的一个温和的非退化条件下素数解个数的渐近性。参数最初通过circle方法进行，但这本身是不够的。为了得到指数和的某些平均值的非平凡界，我们将这些和解释为辛群$operatorname {Sp}_{8}(mathbf{Z}/qmathbf{Z})$ Sp 8 （Z /q Z）的Weil表示的矩阵系数。这样的矩阵系数的平均值然后使用一个放大论证和卷积测度的收敛结果有界，这减少了理解Weil表示中某些12维子群的作用的问题。利用有限域$operatorname {SL}_{2}(k)$ SL 2 (k), $k$ k的基本表示理论可以得到充分的理解。

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引用次数: 0

Sharp Bound for the Erdős–Straus Non-averaging Set Problem Erdős-Straus非平均集问题的夏普界

IF 2.2 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis

Pub Date : 2025-12-03 DOI: 10.1007/s00039-025-00728-8

Huy Tuan Pham, Dmitrii Zakharov

A set of integers

$A$

A is non-averaging if there is no element

$a$

a in

$A$

A which can be written as an average of a subset of

$A$

A not containing

$a$

a . We show that the largest non-averaging subset of

${1, ldots , n}$

{ 1 , … , n } has size

$n^{1/4+o(1)}$

n 1 / 4 + o ( 1 ) , thus solving the Erdős–Straus problem. We also determine the largest size of a non-averaging set in a

$d$

d -dimensional box for any fixed

$d$

d . Our main tool includes the structure theorem for the set of subset sums due to Conlon, Fox and the first author, together with a result about the structure of a point set in nearly convex position.

一组整数$A$ A是非平均的，如果$A$ A$ A中没有元素$A$ A，它可以写成$A$ A的一个子集$A$ A不包含$A$ A的平均值。我们证明了${1,ldots, n}${1，…，n}的最大非平均子集的大小为$n^{1/4+o(1)}$ n 1/4+o(1)，从而解决了Erdős-Straus问题。对于任意固定的d$ d，我们还确定了d$ d维盒子中非平均集的最大大小。我们的主要工具包括Conlon， Fox和第一作者的子集和集的结构定理，以及关于近凸位置点集结构的结果。

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引用次数: 0

Sharpness and Locality for Percolation on Finite Transitive Graphs 有限传递图上渗透的锐性和局部性

IF 2.2 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis

Pub Date : 2025-11-28 DOI: 10.1007/s00039-025-00726-w

Philip Easo

Let $(G_{n}) = left ((V_{n},E_{n})right )$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>V</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>)</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> be a sequence of finite connected vertex-transitive graphs with uniformly bounded vertex degrees such that $lvert V_{n} rvert to infty $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>|</mml:mo> <mml:msub> <mml:mi>V</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>|</mml:mo> <mml:mo>→</mml:mo> <mml:mi>∞</mml:mi> </mml:math> as $n to infty $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> <mml:mo>→</mml:mo> <mml:mi>∞</mml:mi> </mml:math> . We say that percolation on $G_{n}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> has a sharp phase transition (as $n to infty $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> <mml:mo>→</mml:mo> <mml:mi>∞</mml:mi> </mml:math> ) if, as the percolation parameter crosses some critical point, the number of vertices contained in the largest percolation cluster jumps from logarithmic to linear order with high probability. We prove that percolation on $G_{n}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> has a sharp phase transition unless, after passing to a subsequence, the rescaled graph-metric on $G_{n}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> (rapidly) converges to the unit circle with respect to the Gromov-Hausdorff metric. We deduce that under the same hypothesis, the critical point for the emergence of a giant (i.e. linear-sized) cluster in <jats:t

设$(G_{n}) = left ((V_{n},E_{n})right )$ （gn) = (vn, en)）是顶点度一致有界的有限连通顶点传递图序列，使得$lvert V_{n} rvert to infty $ | V n |→∞= $n to infty $ n→∞。如果当渗透参数越过某个临界点时，最大的渗透簇中包含的顶点数高概率地从对数阶跃到线性阶，我们说$G_{n}$ G n上的渗透具有急剧的相变（$n to infty $ n→∞）。我们证明了$G_{n}$ gn上的渗流有一个急剧的相变，除非在传递到子序列之后，$G_{n}$ gn上的重标图度量（迅速）收敛到相对于Gromov-Hausdorff度量的单位圆。我们推断，在相同的假设下，$G_{n}$ G n中出现巨大（即线性大小）集群的临界点与$(G_{n})$ （G n）的Benjamini-Schramm极限中出现无限集群的临界点重合，当该极限存在时。

{"title":"Sharpness and Locality for Percolation on Finite Transitive Graphs","authors":"Philip Easo","doi":"10.1007/s00039-025-00726-w","DOIUrl":"https://doi.org/10.1007/s00039-025-00726-w","url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <jats:tex-math>$(G_{n}) = left ((V_{n},E_{n})right )$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>V</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>)</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> be a sequence of finite connected vertex-transitive graphs with uniformly bounded vertex degrees such that <jats:inline-formula> <jats:alternatives> <jats:tex-math>$lvert V_{n} rvert to infty $</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>|</mml:mo> <mml:msub> <mml:mi>V</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>|</mml:mo> <mml:mo>→</mml:mo> <mml:mi>∞</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> as <jats:inline-formula> <jats:alternatives> <jats:tex-math>$n to infty $</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>n</mml:mi> <mml:mo>→</mml:mo> <mml:mi>∞</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> . We say that percolation on <jats:inline-formula> <jats:alternatives> <jats:tex-math>$G_{n}$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> </jats:alternatives> </jats:inline-formula> has a <jats:italic>sharp</jats:italic> phase transition (as <jats:inline-formula> <jats:alternatives> <jats:tex-math>$n to infty $</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>n</mml:mi> <mml:mo>→</mml:mo> <mml:mi>∞</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> ) if, as the percolation parameter crosses some critical point, the number of vertices contained in the largest percolation cluster jumps from logarithmic to linear order with high probability. We prove that percolation on <jats:inline-formula> <jats:alternatives> <jats:tex-math>$G_{n}$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> </jats:alternatives> </jats:inline-formula> has a sharp phase transition unless, after passing to a subsequence, the rescaled graph-metric on <jats:inline-formula> <jats:alternatives> <jats:tex-math>$G_{n}$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> </jats:alternatives> </jats:inline-formula> (rapidly) converges to the unit circle with respect to the Gromov-Hausdorff metric. We deduce that under the same hypothesis, the critical point for the emergence of a giant (i.e. linear-sized) cluster in <jats:inline-formula> <jats:alternatives> <jats:t","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145610863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Oscillatory Integral Operators and Variable Schrödinger Propagators: Beyond the Universal Estimates 振荡积分算子与变量Schrödinger传播算子：超越一般估计

IF 2.2 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis

Pub Date : 2025-11-19 DOI: 10.1007/s00039-025-00724-y

Mingfeng Chen, Shengwen Gan, Shaoming Guo, Jonathan Hickman, Marina Iliopoulou, James Wright

We consider a class of Hörmander-type oscillatory integral operators in

$mathbb{R}^{n}$

R n for

$n geq 3$

n ≥ 3 odd with real analytic phase. We derive weak conditions on the phase which ensure

$L^{p}$

L p bounds beyond the universal

$p geq 2 cdot frac{n+1}{n-1}$

p ≥ 2 ⋅ n + 1 n − 1 range guaranteed by Stein’s oscillatory integral theorem. This expands and elucidates pioneering work of Bourgain from the early 1990s. We also consider a closely related class of variable coefficient Schrödinger propagator-type operators, and show that the corresponding theory differs significantly from that of the Hörmander-type operators. The main ingredient in the proof is a curved Kakeya/Nikodym maximal function estimate. This is established by combining the polynomial method with certain uniform sublevel set estimates for real analytic functions. The sublevel set estimates are the main novelty in the argument and can be interpreted as a form of quantification of linear independence in the

$C^{omega }$

C ω category.

考虑了在$mathbb{R}^{n}$ R n中，当$n geq 3$ n≥3奇时，一类具有实解析相的Hörmander-type振荡积分算子。我们在相位上导出了保证$L^{p}$ L p界超出Stein振荡积分定理所保证的$p geq 2 cdot frac{n+1}{n-1}$ p≥2⋅n + 1 n−1范围的弱条件。这是对20世纪90年代初布尔甘的开创性工作的扩展和阐释。我们还考虑了一类密切相关的变系数Schrödinger传播算子，并证明了相应的理论与Hörmander-type算子的理论有很大的不同。证明的主要成分是一个弯曲的Kakeya/Nikodym极大函数估计。这是将多项式方法与实解析函数的若干一致子水平集估计相结合建立起来的。子水平集估计是论证中的主要新颖之处，可以解释为$C^{omega }$ C ω类别中线性独立性的一种量化形式。

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