Mathematische Annalen最新文献

{"title":"Sequential topological complexity of aspherical spaces and sectional categories of subgroup inclusions.","authors":"Arturo Espinosa Baro, Michael Farber, Stephan Mescher, John Oprea","doi":"10.1007/s00208-024-03033-1","DOIUrl":"https://doi.org/10.1007/s00208-024-03033-1","url":null,"abstract":"<p><p>We generalize results from topological robotics on the topological complexity (TC) of aspherical spaces to sectional categories of fibrations inducing subgroup inclusions on the level of fundamental groups. In doing so, we establish new lower bounds on sequential TCs of aspherical spaces as well as the parametrized TC of epimorphisms. Moreover, we generalize the Costa-Farber canonical class for TC to classes for sequential TCs and explore their properties. We combine them with the results on sequential TCs of aspherical spaces to obtain results on spaces that are not necessarily aspherical.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"391 3","pages":"4555-4605"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11829864/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143441159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the best constants of Schur multipliers of second order divided difference functions.","authors":"Martijn Caspers, Jesse Reimann","doi":"10.1007/s00208-025-03111-y","DOIUrl":"https://doi.org/10.1007/s00208-025-03111-y","url":null,"abstract":"&lt;p&gt;&lt;p&gt;We give a new proof of the boundedness of bilinear Schur multipliers of second order divided difference functions, as obtained earlier by Potapov, Skripka and Sukochev in their proof of Koplienko's conjecture on the existence of higher order spectral shift functions. Our proof is based on recent methods involving bilinear transference and the Hörmander-Mikhlin-Schur multiplier theorem. Our approach provides a significant sharpening of the known asymptotic bounds of bilinear Schur multipliers of second order divided difference functions. Furthermore, we give a new lower bound of these bilinear Schur multipliers, giving again a fundamental improvement on the best known bounds obtained by Coine, Le Merdy, Potapov, Sukochev and Tomskova. More precisely, we prove that for &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt; &lt;mo&gt;∈&lt;/mo&gt; &lt;msup&gt;&lt;mi&gt;C&lt;/mi&gt; &lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;R&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/mrow&gt; &lt;/math&gt; and &lt;math&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;&lt;&lt;/mo&gt; &lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt; &lt;mo&gt;&lt;&lt;/mo&gt; &lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt; &lt;/math&gt; with &lt;math&gt; &lt;mrow&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt; &lt;mi&gt;p&lt;/mi&gt;&lt;/mfrac&gt; &lt;mo&gt;=&lt;/mo&gt; &lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt; &lt;msub&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt; &lt;/mfrac&gt; &lt;mo&gt;+&lt;/mo&gt; &lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt; &lt;msub&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt; &lt;/mfrac&gt; &lt;/mrow&gt; &lt;/math&gt; we have &lt;dispformula&gt; &lt;math&gt; &lt;mrow&gt; &lt;mtable&gt; &lt;mtr&gt; &lt;mtd&gt; &lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt; &lt;msub&gt;&lt;mi&gt;M&lt;/mi&gt; &lt;msup&gt;&lt;mi&gt;f&lt;/mi&gt; &lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt; &lt;mn&gt;2&lt;/mn&gt; &lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt; &lt;/msup&gt; &lt;/msub&gt; &lt;mo&gt;:&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;S&lt;/mi&gt; &lt;msub&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt; &lt;/msub&gt; &lt;mo&gt;×&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;S&lt;/mi&gt; &lt;msub&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt; &lt;/msub&gt; &lt;mo&gt;→&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;S&lt;/mi&gt; &lt;mi&gt;p&lt;/mi&gt;&lt;/msub&gt; &lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt; &lt;mo&gt;≲&lt;/mo&gt; &lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt; &lt;msup&gt;&lt;mi&gt;f&lt;/mi&gt; &lt;mrow&gt;&lt;mo&gt;'&lt;/mo&gt; &lt;mo&gt;'&lt;/mo&gt;&lt;/mrow&gt; &lt;/msup&gt; &lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt; &lt;mi&gt;∞&lt;/mi&gt;&lt;/msub&gt; &lt;mi&gt;D&lt;/mi&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt; &lt;/mtd&gt; &lt;/mtr&gt; &lt;/mtable&gt; &lt;/mrow&gt; &lt;/math&gt; &lt;/dispformula&gt; where the constant &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; is specified in Theorem 7.1 and &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mn&gt;2&lt;/mn&gt; &lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mn&gt;2&lt;/mn&gt; &lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;≈&lt;/mo&gt; &lt;msup&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt; &lt;msup&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;∗&lt;/mo&gt;&lt;/msup&gt; &lt;/mrow&gt; &lt;/math&gt; with &lt;math&gt;&lt;msup&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;∗&lt;/mo&gt;&lt;/msup&gt; &lt;/math&gt; the Hölder conjugate of &lt;i&gt;p&lt;/i&gt;. We further show that for &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;λ&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt; &lt;mo&gt;=&lt;/mo&gt; &lt;mi&gt;λ&lt;/mi&gt; &lt;mo&gt;|&lt;/mo&gt; &lt;mi&gt;λ&lt;/mi&gt; &lt;mo&gt;|&lt;/mo&gt; &lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt; &lt;mo&gt;∈&lt;/mo&gt; &lt;mi&gt;R&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; for every &lt;math&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;&lt;&lt;/mo&gt; &lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;&lt;&lt;/mo&gt; &lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt; &lt;/math&gt; we have &lt;dispformula&gt; &lt;math&gt; &lt;mrow&gt; &lt;mtable&gt; &lt;mtr&gt; &lt;mtd&gt; &lt;mrow&gt;&lt;msup&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mn&gt;","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 1","pages":"1119-1166"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11971180/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143795741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Polynomial Fourier decay for fractal measures and their pushforwards.","authors":"Simon Baker, Amlan Banaji","doi":"10.1007/s00208-025-03091-z","DOIUrl":"https://doi.org/10.1007/s00208-025-03091-z","url":null,"abstract":"<p><p>We prove that the pushforwards of a very general class of fractal measures <math><mi>μ</mi></math> on <math> <msup><mrow><mi>R</mi></mrow> <mi>d</mi></msup> </math> under a large family of non-linear maps <math><mrow><mi>F</mi> <mo>:</mo> <mspace></mspace> <msup><mrow><mi>R</mi></mrow> <mi>d</mi></msup> <mo>→</mo> <mi>R</mi></mrow> </math> exhibit polynomial Fourier decay: there exist <math><mrow><mi>C</mi> <mo>,</mo> <mi>η</mi> <mo>></mo> <mn>0</mn></mrow> </math> such that <math> <mrow><mrow><mo>|</mo></mrow> <mover><mrow><mi>F</mi> <mi>μ</mi></mrow> <mo>^</mo></mover> <msup> <mrow><mrow><mo>(</mo> <mi>ξ</mi> <mo>)</mo></mrow> <mo>|</mo> <mo>≤</mo> <mi>C</mi> <mo>|</mo> <mi>ξ</mi> <mo>|</mo></mrow> <mrow><mo>-</mo> <mi>η</mi></mrow> </msup> </mrow> </math> for all <math><mrow><mi>ξ</mi> <mo>≠</mo> <mn>0</mn></mrow> </math> . Using this, we prove that if <math><mrow><mi>Φ</mi> <mo>=</mo> <msub><mrow><mo>{</mo> <msub><mi>φ</mi> <mi>a</mi></msub> <mo>:</mo> <mspace></mspace> <mrow><mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo></mrow> <mo>→</mo> <mrow><mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo></mrow> <mo>}</mo></mrow> <mrow><mi>a</mi> <mo>∈</mo> <mi>A</mi></mrow> </msub> </mrow> </math> is an iterated function system consisting of analytic contractions, and there exists <math><mrow><mi>a</mi> <mo>∈</mo> <mi>A</mi></mrow> </math> such that <math><msub><mi>φ</mi> <mi>a</mi></msub> </math> is not an affine map, then every non-atomic self-conformal measure for <math><mi>Φ</mi></math> has polynomial Fourier decay; this result was obtained simultaneously by Algom, Rodriguez Hertz, and Wang. We prove applications related to the Fourier uniqueness problem, Fractal Uncertainty Principles, Fourier restriction estimates, and quantitative equidistribution properties of numbers in fractal sets.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 1","pages":"209-261"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11971211/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143795744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantitative approximate definable choices.","authors":"Antonio Lerario, Luca Rizzi, Daniele Tiberio","doi":"10.1007/s00208-025-03128-3","DOIUrl":"https://doi.org/10.1007/s00208-025-03128-3","url":null,"abstract":"<p><p>In semialgebraic geometry, projections play a prominent role. A <i>definable choice</i> is a semialgebraic selection of one point in every fiber of a projection. Definable choices exist by semialgebraic triviality, but their complexity depends exponentially on the number of variables. By allowing the selection to be approximate (in the Hausdorff sense), we improve on this result. In particular, we construct an approximate selection whose degree is linear in the complexity of the projection and does not depend on the number of variables. This work is motivated by infinite-dimensional applications, in particular to the Sard conjecture in sub-Riemannian geometry. To prove these results, we develop a general quantitative theory for Hausdorff approximations in semialgebraic geometry, which has independent interest.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 1","pages":"1289-1319"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11971197/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143795747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the smooth locus of affine Schubert varieties.","authors":"Georgios Pappas, Rong Zhou","doi":"10.1007/s00208-025-03123-8","DOIUrl":"https://doi.org/10.1007/s00208-025-03123-8","url":null,"abstract":"<p><p>We give a simple and uniform proof of a conjecture of Haines-Richarz characterizing the smooth locus of Schubert varieties in twisted affine Grassmannians. Our method is elementary and avoids any representation theoretic techniques, instead relying on a combinatorial analysis of tangent spaces of Schubert varieties.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 2","pages":"1483-1501"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12084183/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144094315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\"><ns0:math><ns0:msup><ns0:mi>C</ns0:mi> <ns0:mi>∞</ns0:mi></ns0:msup> </ns0:math> regularity in semilinear free boundary problems.","authors":"Daniel Restrepo, Xavier Ros-Oton","doi":"10.1007/s00208-025-03135-4","DOIUrl":"10.1007/s00208-025-03135-4","url":null,"abstract":"<p><p>We study the higher regularity of solutions and free boundaries in the Alt-Phillips problem <math><mrow><mi>Δ</mi> <mi>u</mi> <mo>=</mo> <msup><mi>u</mi> <mrow><mi>γ</mi> <mo>-</mo> <mn>1</mn></mrow> </msup> <mo>,</mo></mrow> </math> with <math><mrow><mi>γ</mi> <mo>∈</mo> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> <mo>.</mo></mrow> </math> Our main results imply that, once free boundaries are <math> <mrow><msup><mi>C</mi> <mrow><mn>1</mn> <mo>,</mo> <mi>α</mi></mrow> </msup> <mo>,</mo></mrow> </math> then they are <math> <mrow><msup><mi>C</mi> <mi>∞</mi></msup> <mo>.</mo></mrow> </math> In addition <math><mrow><mi>u</mi> <mo>/</mo> <msup><mi>d</mi> <mfrac><mn>2</mn> <mrow><mn>2</mn> <mo>-</mo> <mi>γ</mi></mrow> </mfrac> </msup> </mrow> </math> and <math><msup><mi>u</mi> <mfrac><mrow><mn>2</mn> <mo>-</mo> <mi>γ</mi></mrow> <mn>2</mn></mfrac> </msup> </math> are <math><msup><mi>C</mi> <mi>∞</mi></msup> </math> too. In order to achieve this, we need to establish fine regularity estimates for solutions of linear equations with boundary-singular Hardy potentials <math><mrow><mo>-</mo> <mi>Δ</mi> <mi>v</mi> <mo>=</mo> <mi>κ</mi> <mi>v</mi> <mo>/</mo> <msup><mi>d</mi> <mn>2</mn></msup> </mrow> </math> in <math><mrow><mi>Ω</mi> <mo>,</mo></mrow> </math> where <i>d</i> is the distance to the boundary and <math><mrow><mi>κ</mi> <mo>≤</mo> <mfrac><mn>1</mn> <mn>4</mn></mfrac> <mo>.</mo></mrow> </math> Interestingly, we need to include even the critical constant <math><mrow><mi>κ</mi> <mo>=</mo> <mfrac><mn>1</mn> <mn>4</mn></mfrac> <mo>,</mo></mrow> </math> which corresponds to <math><mrow><mi>γ</mi> <mo>=</mo> <mfrac><mn>2</mn> <mn>3</mn></mfrac> <mo>.</mo></mrow></math></p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 3","pages":"3397-3446"},"PeriodicalIF":1.4,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12310783/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144775717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Coarsely holomorphic curves and symplectic topology","authors":"Spencer Cattalani","doi":"10.1007/s00208-024-02985-8","DOIUrl":"https://doi.org/10.1007/s00208-024-02985-8","url":null,"abstract":"<p>A taming symplectic structure provides an upper bound on the area of an approximately pseudoholomorphic curve in terms of its homology class. We prove that, conversely, an almost complex manifold with such an area bound admits a taming symplectic structure. This confirms a speculation by Gromov. We also characterize the cone of taming symplectic structures numerically, prove that complex 2-cycles can be approximated by coarsely holomorphic curves, and provide a lower energy bound for such curves.\u0000</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"31 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multifractality and intermittency in the limit evolution of polygonal vortex filaments","authors":"Valeria Banica, Daniel Eceizabarrena, Andrea R. Nahmod, Luis Vega","doi":"10.1007/s00208-024-02971-0","DOIUrl":"https://doi.org/10.1007/s00208-024-02971-0","url":null,"abstract":"<p>With the aim of quantifying turbulent behaviors of vortex filaments, we study the multifractality and intermittency of the family of generalized Riemann’s non-differentiable functions </p><span>$$begin{aligned} R_{x_0}(t) = sum _{n ne 0} frac{e^{2pi i ( n^2 t + n x_0 ) } }{n^2}, qquad x_0 in [0,1]. end{aligned}$$</span><p>These functions represent, in a certain limit, the trajectory of regular polygonal vortex filaments that evolve according to the binormal flow. When <span>(x_0)</span> is rational, we show that <span>(R_{x_0})</span> is multifractal and intermittent by completely determining the spectrum of singularities of <span>(R_{x_0})</span> and computing the <span>(L^p)</span> norms of its Fourier high-pass filters, which are analogues of structure functions. We prove that <span>(R_{x_0})</span> has a multifractal behavior also when <span>(x_0)</span> is irrational. The proofs rely on a careful design of Diophantine sets that depend on <span>(x_0)</span>, which we study by using the Duffin–Schaeffer theorem and the Mass Transference Principle.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"11 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the uniqueness of periodic solutions for a Rayleigh–Liénard system with impulses","authors":"Hebai Chen, Jie Jin, Zhaoxia Wang, Dongmei Xiao","doi":"10.1007/s00208-024-02996-5","DOIUrl":"https://doi.org/10.1007/s00208-024-02996-5","url":null,"abstract":"<p>This paper is to provide a criterion of the uniqueness of periodic solutions for a Rayleigh-Liénard system with state-dependent impulses. Notice that such results of a planar system with state-dependent impulses are few. Moreover, the Rayleigh-Liénard system with state-dependent impulses has wide applications, such as a simple pendulum and a spring vibrator. Further, we obtain the uniqueness of periodic solutions of the simple pendulum with state-dependent impulses and the spring vibrator with state-dependent impulses by the criterion.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"85 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Uniformly super McDuff $$hbox {II}_1$$ factors","authors":"Isaac Goldbring, David Jekel, Srivatsav Kunnawalkam Elayavalli, Jennifer Pi","doi":"10.1007/s00208-024-02959-w","DOIUrl":"https://doi.org/10.1007/s00208-024-02959-w","url":null,"abstract":"<p>We introduce and study the family of uniformly super McDuff <span>(hbox {II}_1)</span> factors. This family is shown to be closed under elementary equivalence and also coincides with the family of <span>(hbox {II}_1)</span> factors with the Brown property introduced in Atkinson et al. (Adv. Math. 396, 108107, 2022). We show that a certain family of existentially closed factors, the so-called infinitely generic factors, are uniformly super McDuff, thereby improving a recent result of Chifan et al. (Embedding Universality for <span>(hbox {II}_1)</span> Factors with Property (T). arXiv preprint, 2022). We also show that Popa’s family of strongly McDuff <span>(hbox {II}_1)</span> factors are uniformly super McDuff. Lastly, we investigate when finitely generic <span>(hbox {II}_1)</span> factors are uniformly super McDuff.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}