Geometric and Functional Analysis最新文献

A Continuous Cusp Closing Process for Negative Kähler-Einstein Metrics 负Kähler-Einstein指标的连续尖峰关闭过程

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-03-04 DOI: 10.1007/s00039-025-00708-y

Xin Fu, Hans-Joachim Hein, Xumin Jiang

引用次数: 0

On the Shapes of Rational Lemniscates 论理性lemnisces的形状

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-02-18 DOI: 10.1007/s00039-025-00704-2

Christopher J. Bishop, Alexandre Eremenko, Kirill Lazebnik

引用次数: 0

Suppression of Chemotactic Singularity by Buoyancy 浮力对趋化奇异性的抑制

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-02-13 DOI: 10.1007/s00039-025-00706-0

Zhongtian Hu, Alexander Kiselev, Yao Yao

引用次数: 0

Uniqueness of Tangent Flows at Infinity for Finite-Entropy Shortening Curves 有限熵缩短曲线无穷远处切线流动的唯一性

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-02-13 DOI: 10.1007/s00039-025-00705-1

Kyeongsu Choi, Dong-Hwi Seo, Wei-Bo Su, Kai-Wei Zhao

引用次数: 0

On the Spielman-Teng Conjecture 关于斯皮尔伯格-邓猜想

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-02-13 DOI: 10.1007/s00039-025-00707-z

Ashwin Sah, Julian Sahasrabudhe, Mehtaab Sawhney

引用次数: 0

Geometric Langlands Duality for Periods 周期的几何朗兰对偶

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-02-06 DOI: 10.1007/s00039-025-00702-4

Tony Feng, Jonathan Wang

引用次数: 0

Optimal Rigidity and Maximum of the Characteristic Polynomial of Wigner Matrices Wigner矩阵特征多项式的最优刚度和最大值

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-02-05 DOI: 10.1007/s00039-025-00701-5

Paul Bourgade, Patrick Lopatto, Ofer Zeitouni

引用次数: 0

Invariant Subvarieties of Minimal Homological Dimension, Zero Lyapunov Exponents, and Monodromy 最小同调维的不变子变，零Lyapunov指数，和单态

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-02-03 DOI: 10.1007/s00039-025-00700-6

Paul Apisa

引用次数: 0

Unit and Distinct Distances in Typical Norms 典型规范中的单位和不同距离

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-01-24 DOI: 10.1007/s00039-025-00698-x

Noga Alon, Matija Bucić, Lisa Sauermann

{"title":"Unit and Distinct Distances in Typical Norms","authors":"Noga Alon, Matija Bucić, Lisa Sauermann","doi":"10.1007/s00039-025-00698-x","DOIUrl":"https://doi.org/10.1007/s00039-025-00698-x","url":null,"abstract":"Erdős’ unit distance problem and Erdős’ distinct distances problem are among the most classical and well-known open problems in discrete mathematics. They ask for the maximum number of unit distances, or the minimum number of distinct distances, respectively, determined by n points in the Euclidean plane. The question of what happens in these problems if one considers normed spaces other than the Euclidean plane has been raised in the 1980s by Ulam and Erdős and attracted a lot of attention over the years. We give an essentially tight answer to both questions for almost all norms on (mathbb{R}^{d}), in a certain Baire categoric sense.For the unit distance problem we prove that for almost all norms ∥.∥ on (mathbb{R}^{d}), any set of n points defines at most (frac{1}{2} d cdot n log _{2} n) unit distances according to ∥.∥. We also show that this is essentially tight, by proving that for every norm ∥.∥ on (mathbb{R}^{d}), for any large n, we can find n points defining at least (frac{1}{2}(d-1-o(1))cdot n log _{2} n) unit distances according to ∥.∥.For the distinct distances problem, we prove that for almost all norms ∥.∥ on (mathbb{R}^{d}) any set of n points defines at least (1−o(1))n distinct distances according to ∥.∥. This is clearly tight up to the o(1) term.We also answer the famous Hadwiger–Nelson problem for almost all norms on (mathbb{R}^{2}), showing that their unit distance graph has chromatic number 4.Our results settle, in a strong and somewhat surprising form, problems and conjectures of Brass, Matoušek, Brass–Moser–Pach, Chilakamarri, and Robertson. The proofs combine combinatorial and geometric ideas with tools from Linear Algebra, Topology and Algebraic Geometry.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"30 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143026658","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

Lagrangian Subvarieties of Hyperspherical Varieties 超球变种的拉格朗日子变种

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-01-22 DOI: 10.1007/s00039-025-00703-3

Michael Finkelberg, Victor Ginzburg, Roman Travkin

引用次数: 0