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Commutator type and Levi type of a system of CR vector fields CR矢量场系统的换向子型和李维型
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-24 DOI: 10.1016/j.matpur.2025.103693
Xiaojun Huang , Wanke Yin
{"title":"Commutator type and Levi type of a system of CR vector fields","authors":"Xiaojun Huang ,&nbsp;Wanke Yin","doi":"10.1016/j.matpur.2025.103693","DOIUrl":"10.1016/j.matpur.2025.103693","url":null,"abstract":"<div><div>Let <em>M</em> be a smooth pseudoconvex real hypersurface in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span> and let <em>B</em> be a subbundle of the CR tangent vector bundle of <em>M</em>. We prove that the commutator type and the Levi type associated with <em>B</em> are the same when either of them is less than 8. When the Levi type is eight or larger, we show that it is bounded from above by twice of the commutator type minus 8. Our results provide a partial solution to a generalized conjecture of D'Angelo.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"196 ","pages":"Article 103693"},"PeriodicalIF":2.1,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143507536","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
Frequency-domain criterion on the stabilizability for infinite-dimensional linear control systems 无穷维线性控制系统稳定性的频域判据
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-24 DOI: 10.1016/j.matpur.2025.103690
Karl Kunisch , Gengsheng Wang , Huaiqiang Yu
{"title":"Frequency-domain criterion on the stabilizability for infinite-dimensional linear control systems","authors":"Karl Kunisch ,&nbsp;Gengsheng Wang ,&nbsp;Huaiqiang Yu","doi":"10.1016/j.matpur.2025.103690","DOIUrl":"10.1016/j.matpur.2025.103690","url":null,"abstract":"<div><div>A quantitative frequency-domain condition related to the exponential stabilizability for infinite-dimensional linear control systems is presented. It is proven that this condition is necessary and sufficient for the stabilizability of special systems, while it is a necessary condition for the stabilizability in general. Applications are provided.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"196 ","pages":"Article 103690"},"PeriodicalIF":2.1,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143507535","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
Derived categories of symmetric products and moduli spaces of vector bundles on a curve 曲线上向量束的对称积和模空间的导出范畴
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-24 DOI: 10.1016/j.matpur.2025.103694
Kyoung-Seog Lee , Han-Bom Moon
{"title":"Derived categories of symmetric products and moduli spaces of vector bundles on a curve","authors":"Kyoung-Seog Lee ,&nbsp;Han-Bom Moon","doi":"10.1016/j.matpur.2025.103694","DOIUrl":"10.1016/j.matpur.2025.103694","url":null,"abstract":"<div><div>We show that the derived categories of symmetric products of a curve are embedded into the derived categories of the moduli spaces of vector bundles of large ranks on the curve. It supports a prediction of the existence of a semiorthogonal decomposition of the derived category of the moduli space, expected by a motivic computation. As an application, we show that all Jacobian varieties, symmetric products of curves, and all principally polarized abelian varieties of dimension at most three, are Fano visitors. We also obtain similar results for motives.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"197 ","pages":"Article 103694"},"PeriodicalIF":2.1,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509395","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
Damping for fractional wave equations and applications to water waves 分数波方程的阻尼及其在水波中的应用
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-24 DOI: 10.1016/j.matpur.2025.103692
Thomas Alazard , Jeremy L. Marzuola , Jian Wang
{"title":"Damping for fractional wave equations and applications to water waves","authors":"Thomas Alazard ,&nbsp;Jeremy L. Marzuola ,&nbsp;Jian Wang","doi":"10.1016/j.matpur.2025.103692","DOIUrl":"10.1016/j.matpur.2025.103692","url":null,"abstract":"<div><div>Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give the explicit decay rates for the energy, but do not address reflection/transmission of waves at the interface of the damping. Still for a subset of the models considered, this represents the first result proving the decay of the energy of the surface wave models.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"196 ","pages":"Article 103692"},"PeriodicalIF":2.1,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529175","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
Four-dimensional gradient Ricci solitons with (half) nonnegative isotropic curvature 具有（半）非负各向同性曲率的四维梯度里奇孤子
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-24 DOI: 10.1016/j.matpur.2025.103686
Huai-Dong Cao , Junming Xie
{"title":"Four-dimensional gradient Ricci solitons with (half) nonnegative isotropic curvature","authors":"Huai-Dong Cao ,&nbsp;Junming Xie","doi":"10.1016/j.matpur.2025.103686","DOIUrl":"10.1016/j.matpur.2025.103686","url":null,"abstract":"<div><div>This is a sequel to our paper <span><span>[24]</span></span>, in which we investigated the geometry of 4-dimensional gradient shrinking Ricci solitons with half positive (nonnegative) isotropic curvature. In this paper, we mainly focus on 4-dimensional gradient steady Ricci solitons with nonnegative isotropic curvature (WPIC) or half nonnegative isotropic curvature (half WPIC). In particular, for 4D complete <em>ancient solutions</em> with WPIC, we are able to prove the 2-nonnegativity of the Ricci curvature and bound the curvature tensor <em>Rm</em> by <span><math><mo>|</mo><mi>R</mi><mi>m</mi><mo>|</mo><mo>≤</mo><mi>R</mi></math></span>. For 4D gradient steady solitons with WPIC, we obtain a classification result. We also give a partial classification of 4D gradient steady Ricci solitons with half WPIC. Moreover, we obtain a preliminary classification result for 4D complete gradient <em>expanding Ricci solitons</em> with WPIC. Finally, motivated by the recent work <span><span>[59]</span></span>, we improve our earlier results in <span><span>[24]</span></span> on 4D gradient <em>shrinking Ricci solitons</em> with half PIC or half WPIC, and also provide a characterization of complete gradient Kähler-Ricci shrinkers in complex dimension two among 4-dimensional gradient Ricci shrinkers.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"197 ","pages":"Article 103686"},"PeriodicalIF":2.1,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511264","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
Non-uniqueness & inadmissibility of the vanishing viscosity limit of the passive scalar transport equation 被动标量输运方程黏度消失极限的非唯一性和不可容许性
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-21 DOI: 10.1016/j.matpur.2025.103685
L. Huysmans , Edriss S. Titi
{"title":"Non-uniqueness & inadmissibility of the vanishing viscosity limit of the passive scalar transport equation","authors":"L. Huysmans ,&nbsp;Edriss S. Titi","doi":"10.1016/j.matpur.2025.103685","DOIUrl":"10.1016/j.matpur.2025.103685","url":null,"abstract":"<div><div>We study the vanishing viscosity/diffusivity limit for the transport of a passive scalar <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mi>R</mi></math></span> by a bounded, divergence-free vector field <span><math><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. This is described by the Cauchy problem to the PDE <span><math><mfrac><mrow><mo>∂</mo><mi>f</mi></mrow><mrow><mo>∂</mo><mi>t</mi></mrow></mfrac><mo>+</mo><mi>∇</mi><mo>⋅</mo><mo>(</mo><mi>u</mi><mi>f</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span>, or with viscosity <span><math><mi>ν</mi><mo>&gt;</mo><mn>0</mn></math></span>, to the PDE <span><math><mfrac><mrow><mo>∂</mo><mi>f</mi></mrow><mrow><mo>∂</mo><mi>t</mi></mrow></mfrac><mo>+</mo><mi>∇</mi><mo>⋅</mo><mo>(</mo><mi>u</mi><mi>f</mi><mo>)</mo><mo>−</mo><mi>ν</mi><mi>Δ</mi><mi>f</mi><mo>=</mo><mn>0</mn></math></span>. In the first part of this work, we construct a bounded, divergence-free vector field <span><math><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></math></span> for which, for any non-constant initial datum, the viscous solutions along different subsequences of the vanishing viscosity limit converge to different solutions to the inviscid problem. In the second part, we construct another bounded, divergence-free vector field <span><math><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></math></span> for which, for every initial datum, the vanishing viscosity limit of solutions exists, is unique, and converges to an inviscid solution; however, when the initial datum is not constant, this inviscid limit is physically inadmissible due to increasing energy/entropy.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"198 ","pages":"Article 103685"},"PeriodicalIF":2.1,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Wigdersons' approach to the uncertainty principle 论威格森对测不准原理的研究
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-21 DOI: 10.1016/j.matpur.2025.103689
Nuno Costa Dias , Franz Luef , João Nuno Prata
{"title":"On Wigdersons' approach to the uncertainty principle","authors":"Nuno Costa Dias ,&nbsp;Franz Luef ,&nbsp;João Nuno Prata","doi":"10.1016/j.matpur.2025.103689","DOIUrl":"10.1016/j.matpur.2025.103689","url":null,"abstract":"<div><div>We revisit the uncertainty principle from the point of view suggested by A. Wigderson and Y. Wigderson. This approach is based on a primary uncertainty principle from which one can derive several inequalities expressing the impossibility of a simultaneous sharp localization in time and frequency. Moreover, it requires no specific properties of the Fourier transform and can therefore be easily applied to all operators satisfying the primary uncertainty principle. A. Wigderson and Y. Wigderson also suggested many generalizations to higher dimensions and stated several conjectures which we address in the present paper. We argue that we have to consider a more general primary uncertainty principle to prove the results suggested by the authors. As a by-product we obtain some new inequalities akin to the Cowling-Price uncertainty principle, a generalization of the Heisenberg uncertainty principle, and derive the entropic uncertainty principle from the primary uncertainty principles.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"198 ","pages":"Article 103689"},"PeriodicalIF":2.1,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534555","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
Cylindrical estimates for the Cheeger constant and applications 契格常数的圆柱形估计及其应用
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI: 10.1016/j.matpur.2024.103633
Aldo Pratelli , Giorgio Saracco
{"title":"Cylindrical estimates for the Cheeger constant and applications","authors":"Aldo Pratelli ,&nbsp;Giorgio Saracco","doi":"10.1016/j.matpur.2024.103633","DOIUrl":"10.1016/j.matpur.2024.103633","url":null,"abstract":"<div><div>We prove a lower bound for the Cheeger constant of a cylinder <span><math><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>L</mi><mo>)</mo></math></span>, where Ω is an open and bounded set. As a consequence, we obtain existence of minimizers for the shape functional defined as the ratio between the first Dirichlet eigenvalue of the <em>p</em>-Laplacian and the <em>p</em>-th power of the Cheeger constant, within the class of bounded convex sets in any <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>. This positively solves open conjectures raised by Parini (<em>J. Convex Anal.</em> (2017)) and by Briani–Buttazzo–Prinari (<em>Ann. Mat. Pura Appl.</em> (2023)).</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"194 ","pages":"Article 103633"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143146799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Formation of trapped surfaces in the Einstein-Yang-Mills system 爱因斯坦-杨-米尔斯系统中捕获面的形成
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI: 10.1016/j.matpur.2025.103661
Nikolaos Athanasiou , Puskar Mondal , Shing-Tung Yau
{"title":"Formation of trapped surfaces in the Einstein-Yang-Mills system","authors":"Nikolaos Athanasiou ,&nbsp;Puskar Mondal ,&nbsp;Shing-Tung Yau","doi":"10.1016/j.matpur.2025.103661","DOIUrl":"10.1016/j.matpur.2025.103661","url":null,"abstract":"<div><div>We prove a scale-invariant, semi-global existence result and a trapped surface formation result in the context of coupled Einstein-Yang-Mills theory, without symmetry assumptions. More precisely, we prove a scale-invariant semi-global existence theorem and show that the focusing of the gravitational and/or chromoelectric-chromomagnetic waves could lead to the formation of a trapped surface. Adopting the signature for decay rates approach introduced in <span><span>[1]</span></span>, we develop a novel gauge (and scale) invariant hierarchy of non-linear estimates for the Yang-Mills curvature which, together with the estimates for the gravitational degrees of freedom, yields the desired semi-global existence result. Once semi-global existence has been established, the formation of a trapped surface follows from a standard ODE argument.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"194 ","pages":"Article 103661"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143146801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Homogenization of non-autonomous evolution problems for convolution type operators in randomly evolving media 随机演化介质中卷积算子非自治演化问题的均匀化
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI: 10.1016/j.matpur.2025.103660
A. Piatnitski , E. Zhizhina
{"title":"Homogenization of non-autonomous evolution problems for convolution type operators in randomly evolving media","authors":"A. Piatnitski ,&nbsp;E. Zhizhina","doi":"10.1016/j.matpur.2025.103660","DOIUrl":"10.1016/j.matpur.2025.103660","url":null,"abstract":"<div><div>We study homogenization problem for non-autonomous parabolic equations of the form <span><math><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>=</mo><mi>L</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>u</mi></math></span> with an integral convolution type operator <span><math><mi>L</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> that has a non-symmetric jump kernel which is periodic in spatial variables and stationary random in time. We show that asymptotically the spatial and temporal evolutions of the solutions are getting decoupled and can be described separately, and, under additional mixing conditions on the coefficient, the homogenized equation is a SPDE with a finite dimensional multiplicative noise.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"194 ","pages":"Article 103660"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143146971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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