Geometric and Functional Analysis最新文献_第2页

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

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-12-05 DOI: 10.1007/s00039-025-00727-9

Ben Green

{"title":"Quadratic Forms in 8 Prime Variables","authors":"Ben Green","doi":"10.1007/s00039-025-00727-9","DOIUrl":"https://doi.org/10.1007/s00039-025-00727-9","url":null,"abstract":"We give an asymptotic for the number of prime solutions to $Q(x_{1},dots , x_{8}) = N$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Q</mml:mi> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>8</mml:mn> </mml:msub> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>N</mml:mi> </mml:math> , subject to a mild non-degeneracy condition on the homogeneous quadratic form $Q$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Q</mml:mi> </mml:math> . 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 $operatorname {Sp}_{8}(mathbf{Z}/qmathbf{Z})$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mo>Sp</mml:mo> <mml:mn>8</mml:mn> </mml:msub> <mml:mo>(</mml:mo> <mml:mi>Z</mml:mi> <mml:mo>/</mml:mo> <mml:mi>q</mml:mi> <mml:mi>Z</mml:mi> <mml:mo>)</mml:mo> </mml:math> . 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 $operatorname {SL}_{2}(k)$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mo>SL</mml:mo> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>(</mml:mo> <mml:mi>k</mml:mi> <mml:mo>)</mml:mo> </mml:math> , $k$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>k</mml:mi> </mml:math> a finite field.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"56 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145680180","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

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

Geometric and Functional Analysis Pub Date : 2025-12-03 DOI: 10.1007/s00039-025-00728-8

Huy Tuan Pham, Dmitrii Zakharov

{"title":"Sharp Bound for the Erdős–Straus Non-averaging Set Problem","authors":"Huy Tuan Pham, Dmitrii Zakharov","doi":"10.1007/s00039-025-00728-8","DOIUrl":"https://doi.org/10.1007/s00039-025-00728-8","url":null,"abstract":"A set of integers $A$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>A</mml:mi> </mml:math> is non-averaging if there is no element $a$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>a</mml:mi> </mml:math> in $A$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>A</mml:mi> </mml:math> which can be written as an average of a subset of $A$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>A</mml:mi> </mml:math> not containing $a$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>a</mml:mi> </mml:math> . We show that the largest non-averaging subset of ${1, ldots , n}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>{</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> <mml:mo>}</mml:mo> </mml:math> has size $n^{1/4+o(1)}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>n</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> <mml:mo>+</mml:mo> <mml:mi>o</mml:mi> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:msup> </mml:math> , thus solving the Erdős–Straus problem. We also determine the largest size of a non-averaging set in a $d$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>d</mml:mi> </mml:math> -dimensional box for any fixed $d$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>d</mml:mi> </mml:math> . 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.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"140 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145657528","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

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

Geometric and Functional Analysis Pub Date : 2025-11-28 DOI: 10.1007/s00039-025-00726-w

Philip Easo

{"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

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

{"title":"Oscillatory Integral Operators and Variable Schrödinger Propagators: Beyond the Universal Estimates","authors":"Mingfeng Chen, Shengwen Gan, Shaoming Guo, Jonathan Hickman, Marina Iliopoulou, James Wright","doi":"10.1007/s00039-025-00724-y","DOIUrl":"https://doi.org/10.1007/s00039-025-00724-y","url":null,"abstract":"We consider a class of Hörmander-type oscillatory integral operators in $mathbb{R}^{n}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>R</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:math> for $n geq 3$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:math> odd with real analytic phase. We derive weak conditions on the phase which ensure $L^{p}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:math> bounds beyond the universal $p geq 2 cdot frac{n+1}{n-1}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>p</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> <mml:mo>⋅</mml:mo> <mml:mfrac> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfrac> </mml:math> 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 $C^{omega }$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>C</mml:mi> <mml:mi>ω</mml:mi> </mml:msup> </mml:math> category.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"19 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145545972","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

Nonnegative Cross-Curvature in Infinite Dimensions: Synthetic Definition and Spaces of Measures 无限维的非负交叉曲率：综合定义和测度空间

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-11-11 DOI: 10.1007/s00039-025-00725-x

Flavien Léger, Gabriele Todeschi, François-Xavier Vialard

引用次数: 0

$mathbb{H}^{p,q}$-Convex Cocompactness and Higher Higher Teichmüller Spaces $mathbb{H}^{p,q}$-凸紧性与Higher Higher teichmller空间

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-11-11 DOI: 10.1007/s00039-025-00719-9

Jonas Beyrer, Fanny Kassel

引用次数: 0

Circle Bundles with PSC over Large Manifolds 圆束与PSC在大型歧管

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-10-31 DOI: 10.1007/s00039-025-00723-z

Aditya Kumar, Balarka Sen

引用次数: 0

Mixing for Dynamical Systems Driven by Stationary Noises 由平稳噪声驱动的动力系统的混合

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-10-10 DOI: 10.1007/s00039-025-00722-0

Sergei Kuksin, Armen Shirikyan

{"title":"Mixing for Dynamical Systems Driven by Stationary Noises","authors":"Sergei Kuksin, Armen Shirikyan","doi":"10.1007/s00039-025-00722-0","DOIUrl":"https://doi.org/10.1007/s00039-025-00722-0","url":null,"abstract":"The paper deals with the problem of long-time asymptotic behaviour of solutions for classes of ODEs and PDEs, perturbed by stationary noises. The latter are not assumed to be <inline-formula><alternatives><mml:math><mml:mi>δ</mml:mi></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$delta $end{document}</tex-math><inline-graphic mime-subtype=\"GIF\" specific-use=\"web\" xlink:href=\"39_2025_722_Article_IEq1.gif\"></inline-graphic></alternatives></inline-formula>-correlated in time, therefore the evolution in question is not necessarily Markovian. We first prove an abstract result which implies the mixing for random dynamical systems satisfying appropriate dissipativity and controllability conditions. It is applicable to a large class of evolution equations, and we illustrate this on the examples of a chain of anharmonic oscillators coupled to heat reservoirs, the 2d Navier–Stokes system, and a complex Ginzburg–Landau equation. Our results also apply to the general theory of random processes on the 1d lattice and allow one to get for them results related to Dobrushin’s theorems on reconstructing processes via their conditional distributions. The proof is based on an iterative construction with Newton’s quadratic approximation. It uses the method of Kantorovich functional, introduced earlier by the authors in the context of randomly forced PDEs, and some ideas used by them in the Markovian case to prove mixing with the help of controllability properties of an associated system.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"186 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145914890","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

Spherical Caps do Not Always Maximize Neumann Eigenvalues on the Sphere 球帽并不总是最大化球上的诺伊曼特征值

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-10-10 DOI: 10.1007/s00039-025-00721-1

Dorin Bucur, Richard S. Laugesen, Eloi Martinet, Mickaël Nahon

引用次数: 0

Affirmative Resolution of Bourgain’s Slicing Problem Using Guan’s Bound 用关界肯定解Bourgain的切片问题

IF 2.2 1区数学

Geometric and Functional Analysis Pub Date : 2025-09-01 DOI: 10.1007/s00039-025-00718-w

Boaz Klartag, Joseph Lehec

{"title":"Affirmative Resolution of Bourgain’s Slicing Problem Using Guan’s Bound","authors":"Boaz Klartag, Joseph Lehec","doi":"10.1007/s00039-025-00718-w","DOIUrl":"https://doi.org/10.1007/s00039-025-00718-w","url":null,"abstract":"<p>We provide the final step in the resolution of Bourgain’s slicing problem in the affirmative. Thus we establish the following theorem: for any convex body <span><span style=\"\">K subseteq mathbb{R}^{n}</span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.313ex\" role=\"img\" style=\"vertical-align: -0.505ex;\" viewbox=\"0 -778.3 3470.7 995.9\" width=\"8.061ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-4B\" y=\"0\"></use><use x=\"1167\" xlink:href=\"#MJMAIN-2286\" y=\"0\"></use><g transform=\"translate(2223,0)\"><use x=\"0\" xlink:href=\"#MJAMS-52\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1021\" xlink:href=\"#MJMATHI-6E\" y=\"581\"></use></g></g></svg></span><script type=\"math/tex\">K subseteq mathbb{R}^{n}</script></span> of volume one, there exists a hyperplane <span><span style=\"\">H subseteq mathbb{R}^{n}</span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.309ex\" role=\"img\" style=\"vertical-align: -0.505ex;\" viewbox=\"0 -777 3469.7 994.3\" width=\"8.059ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-48\" y=\"0\"></use><use x=\"1166\" xlink:href=\"#MJMAIN-2286\" y=\"0\"></use><g transform=\"translate(2222,0)\"><use x=\"0\" xlink:href=\"#MJAMS-52\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1021\" xlink:href=\"#MJMATHI-6E\" y=\"581\"></use></g></g></svg></span><script type=\"math/tex\">H subseteq mathbb{R}^{n}</script></span> such that </p><span><span style=\"\"> Vol_{n-1}(K cap H) > c, </span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.614ex\" role=\"img\" style=\"vertical-align: -0.706ex;\" viewbox=\"0 -821.4 8697.5 1125.3\" width=\"20.201ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-56\" y=\"0\"></use><use x=\"769\" xlink:href=\"#MJMATHI-6F\" y=\"0\"></use><g transform=\"translate(1255,0)\"><use x=\"0\" xlink:href=\"#MJMATHI-6C\" y=\"0\"></use><g transform=\"translate(298,-150)\"><use transform=\"scale(0.707)\" x=\"0\" xlink:href=\"#MJMATHI-6E\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"600\" xlink:href=\"#MJMAIN-2212\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1379\" xlink:href=\"#MJMAIN-31\" y=\"0\"></use></g></g><use x=\"2982\" xlink:href=\"#MJMAIN-28\" y=\"0\"></use><use x=\"3372\" xlink:href=\"#MJMATHI-4B\" y=\"0\"></use><use x=\"4483\" xlink:href=\"#MJMAIN-2229\" y=\"0\"></use><use x=\"5373\" xlink:href=\"#MJMATHI-48\" y=\"0\"></use><use x=\"6261\" xlink:href=\"#MJMAIN-29\" y=\"0\"></use><use x=\"6929\" xlink:href=\"#MJMAIN-3E\" y=\"0\"></use><use x=\"7985\" xlink:href=\"#MJMATHI-63\" y=\"0\"></use><use x=\"8419\" xlink:href=\"#MJMAIN-2C\" y=\"0\"></use></g></svg></span><script type=\"math/tex; mode=display\"> Vol_{n-1}(K cap H) >","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"28 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924666","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