Geometric and Functional Analysis最新文献

{"title":"Lossless Strichartz and Spectral Projection Estimates on Unbounded Manifolds","authors":"Xiaoqi Huang, Christopher D. Sogge, Zhongkai Tao, Zhexing Zhang","doi":"10.1007/s00039-026-00732-6","DOIUrl":"https://doi.org/10.1007/s00039-026-00732-6","url":null,"abstract":"","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"43 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146230757","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}

{"title":"Strong Asymptotic Freeness of Haar Unitaries in Quasi-Exponential Dimensional Representations","authors":"Michael Magee, Mikael de la Salle","doi":"10.1007/s00039-026-00730-8","DOIUrl":"https://doi.org/10.1007/s00039-026-00730-8","url":null,"abstract":"We prove almost sure strong asymptotic freeness of i.i.d. random unitaries with the following law: sample a Haar unitary matrix of dimension <jats:inline-formula> <jats:alternatives> <jats:tex-math>$n$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>n</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> and then send this unitary into an irreducible representation of <jats:inline-formula> <jats:alternatives> <jats:tex-math>$mathrm{U}(n)$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>U</mml:mi> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:math> </jats:alternatives> </jats:inline-formula> . The strong convergence holds as long as the irreducible representation arises from a pair of partitions of total size at most <jats:inline-formula> <jats:alternatives> <jats:tex-math>$n^{frac{1}{42}-varepsilon }$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>n</mml:mi> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mn>42</mml:mn> </mml:mfrac> <mml:mo>−</mml:mo> <mml:mi>ε</mml:mi> </mml:mrow> </mml:msup> </mml:math> </jats:alternatives> </jats:inline-formula> and is uniform in this regime. Previously this was known for partitions of total size up to <jats:inline-formula> <jats:alternatives> <jats:tex-math>$asymp log n/log log n$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>≍</mml:mo> <mml:mo>log</mml:mo> <mml:mi>n</mml:mi> <mml:mo>/</mml:mo> <mml:mo>log</mml:mo> <mml:mo>log</mml:mo> <mml:mi>n</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> by a result of Bordenave and Collins.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"50 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146230771","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}

{"title":"Deformations of $mathbb{Z}_{2}$-Harmonic Spinors on 3-Manifolds","authors":"Gregory J. Parker","doi":"10.1007/s00039-026-00729-1","DOIUrl":"https://doi.org/10.1007/s00039-026-00729-1","url":null,"abstract":"","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"20 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146204951","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}

{"title":"Complete Classification of the Dehn Functions of Bestvina–Brady Groups","authors":"Yu-Chan Chang, Jerónimo García-Mejía, Matteo Migliorini","doi":"10.1007/s00039-026-00731-7","DOIUrl":"https://doi.org/10.1007/s00039-026-00731-7","url":null,"abstract":"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.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"73 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146101776","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}

{"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 <jats:inline-formula> <jats:alternatives> <jats:tex-math>$Q(x_{1},dots , x_{8}) = N$</jats:tex-math> <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> </jats:alternatives> </jats:inline-formula> , subject to a mild non-degeneracy condition on the homogeneous quadratic form <jats:inline-formula> <jats:alternatives> <jats:tex-math>$Q$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Q</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> . 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 <jats:inline-formula> <jats:alternatives> <jats:tex-math>$operatorname {Sp}_{8}(mathbf{Z}/qmathbf{Z})$</jats:tex-math> <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> </jats:alternatives> </jats:inline-formula> . 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 <jats:inline-formula> <jats:alternatives> <jats:tex-math>$operatorname {SL}_{2}(k)$</jats:tex-math> <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> </jats:alternatives> </jats:inline-formula> , <jats:inline-formula> <jats:alternatives> <jats:tex-math>$k$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>k</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> 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}

{"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 <jats:inline-formula> <jats:alternatives> <jats:tex-math>$A$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>A</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> is <jats:italic>non-averaging</jats:italic> if there is no element <jats:inline-formula> <jats:alternatives> <jats:tex-math>$a$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>a</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> in <jats:inline-formula> <jats:alternatives> <jats:tex-math>$A$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>A</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> which can be written as an average of a subset of <jats:inline-formula> <jats:alternatives> <jats:tex-math>$A$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>A</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> not containing <jats:inline-formula> <jats:alternatives> <jats:tex-math>$a$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>a</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> . We show that the largest non-averaging subset of <jats:inline-formula> <jats:alternatives> <jats:tex-math>${1, ldots , n}$</jats:tex-math> <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> </jats:alternatives> </jats:inline-formula> has size <jats:inline-formula> <jats:alternatives> <jats:tex-math>$n^{1/4+o(1)}$</jats:tex-math> <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> </jats:alternatives> </jats:inline-formula> , thus solving the Erdős–Straus problem. We also determine the largest size of a non-averaging set in a <jats:inline-formula> <jats:alternatives> <jats:tex-math>$d$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>d</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> -dimensional box for any fixed <jats:inline-formula> <jats:alternatives> <jats:tex-math>$d$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>d</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> . 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}

{"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 &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:tex-math&gt;$(G_{n}) = left ((V_{n},E_{n})right )$&lt;/jats:tex-math&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;V&lt;/mml:mi&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;E&lt;/mml:mi&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; be a sequence of finite connected vertex-transitive graphs with uniformly bounded vertex degrees such that &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:tex-math&gt;$lvert V_{n} rvert to infty $&lt;/jats:tex-math&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mo&gt;|&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;V&lt;/mml:mi&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;|&lt;/mml:mo&gt; &lt;mml:mo&gt;→&lt;/mml:mo&gt; &lt;mml:mi&gt;∞&lt;/mml:mi&gt; &lt;/mml:math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; as &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:tex-math&gt;$n to infty $&lt;/jats:tex-math&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;mml:mo&gt;→&lt;/mml:mo&gt; &lt;mml:mi&gt;∞&lt;/mml:mi&gt; &lt;/mml:math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; . We say that percolation on &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:tex-math&gt;$G_{n}$&lt;/jats:tex-math&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;/mml:math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; has a &lt;jats:italic&gt;sharp&lt;/jats:italic&gt; phase transition (as &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:tex-math&gt;$n to infty $&lt;/jats:tex-math&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;mml:mo&gt;→&lt;/mml:mo&gt; &lt;mml:mi&gt;∞&lt;/mml:mi&gt; &lt;/mml:math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; ) if, as the percolation parameter crosses some critical point, the number of vertices contained in the largest percolation cluster jumps from logarithmic to linear order with high probability. We prove that percolation on &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:tex-math&gt;$G_{n}$&lt;/jats:tex-math&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;/mml:math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; has a sharp phase transition unless, after passing to a subsequence, the rescaled graph-metric on &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:tex-math&gt;$G_{n}$&lt;/jats:tex-math&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;/mml:math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; (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 &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;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}

{"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 <jats:inline-formula> <jats:alternatives> <jats:tex-math>$mathbb{R}^{n}$</jats:tex-math> <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> </jats:alternatives> </jats:inline-formula> for <jats:inline-formula> <jats:alternatives> <jats:tex-math>$n geq 3$</jats:tex-math> <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> </jats:alternatives> </jats:inline-formula> odd with real analytic phase. We derive weak conditions on the phase which ensure <jats:inline-formula> <jats:alternatives> <jats:tex-math>$L^{p}$</jats:tex-math> <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> </jats:alternatives> </jats:inline-formula> bounds beyond the universal <jats:inline-formula> <jats:alternatives> <jats:tex-math>$p geq 2 cdot frac{n+1}{n-1}$</jats:tex-math> <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> </jats:alternatives> </jats:inline-formula> 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 <jats:inline-formula> <jats:alternatives> <jats:tex-math>$C^{omega }$</jats:tex-math> <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> </jats:alternatives> </jats:inline-formula> 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}

{"title":"Nonnegative Cross-Curvature in Infinite Dimensions: Synthetic Definition and Spaces of Measures","authors":"Flavien Léger, Gabriele Todeschi, François-Xavier Vialard","doi":"10.1007/s00039-025-00725-x","DOIUrl":"https://doi.org/10.1007/s00039-025-00725-x","url":null,"abstract":"","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145485494","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}

{"title":"$mathbb{H}^{p,q}$-Convex Cocompactness and Higher Higher Teichmüller Spaces","authors":"Jonas Beyrer, Fanny Kassel","doi":"10.1007/s00039-025-00719-9","DOIUrl":"https://doi.org/10.1007/s00039-025-00719-9","url":null,"abstract":"","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"2 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145485495","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}