Mathematische Nachrichten最新文献

{"title":"Global Existence and Asymptotic Behavior of Strong Solutions to the 3D Viscous Liquid–Gas Two-Phase Flow Model With Slip Boundary Condition","authors":"Hao Liu","doi":"10.1002/mana.70151","DOIUrl":"https://doi.org/10.1002/mana.70151","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper addresses the existence and large-time asymptotic behavior of strong solutions to the viscous liquid–gas two-phase flow model subject to slip boundary conditions in a three-dimensional, simply connected bounded domain with a smooth boundary consisting of finite number 2D connected components. Compared to the Cauchy problem studied in Yu [<i>Journal of Differential Equations</i> 272 (2021): 732–759] and Guo et al. [<i>Journal of Mathematical Physics</i> 52 (2011): 9], the main advancement lies in overcoming key difficulties involving boundary integral estimates. We establish the global existence and uniqueness of strong solutions for the system provided that the initial energy is sufficiently small. Moreover, we characterize the large-time decay of these solutions. Notably, our analysis allows for initial densities exhibiting large oscillations and including vacuum states.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 6","pages":"1446-1479"},"PeriodicalIF":0.8,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148160801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lower Bounds of Possible Blow-Up Solutions of the Electron Magnetohydrodynamics Equations","authors":"Yulin Ye,&nbsp;Yanqing Wang","doi":"10.1002/mana.70146","DOIUrl":"https://doi.org/10.1002/mana.70146","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;In this paper, we investigate the blow-up rates of strong solutions to the electron magnetohydrodynamics (EMHD) equations. The optimal lower bounds of potential blow-up solutions of the EMHD equations in homogeneous Sobolev spaces &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mover&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mo&gt;̇&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$dot{H}^{s}(mathbb {R}^{n})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; are shown, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$n/2&lt;s&lt;(n+2)/2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for spatial dimensions &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$n=2, 3$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Moreover, for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;≥&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$ sge (n+2)/2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, the blow-up rates of solutions in this system in spaces &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mover&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mo&gt;̇&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$dot{H}^{s}(mathbb {R}^{n})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; are also obtained. The ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 6","pages":"1350-1357"},"PeriodicalIF":0.8,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148160633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Blowup Criterion for the Navier–Stokes Equations via the Middle Eigenvalue of the Strain Tensor in the Anisotropic Besov Spaces With Negative Indices","authors":"Chol-Jun O,&nbsp;Fan Wu","doi":"10.1002/mana.70139","DOIUrl":"https://doi.org/10.1002/mana.70139","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we study blowup criteria for the three-dimensional incompressible Navier–Stokes equations in terms of the middle eigenvalue of the strain tensor. It is known that regularity criteria involving eigenvalues of the strain tensor were first investigated by Neustupa and Penel, and later developed by Miller and others. First, we extend the known blowup criterion in anisotropic Lebesgue spaces by removing the restriction on the admissible exponent range. More precisely, the condition <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mi>q</mi>\u0000 <mo>,</mo>\u0000 <mi>r</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$p,q,r&gt;2$</annotation>\u0000 </semantics></math> appearing in previous results is relaxed to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mi>q</mi>\u0000 <mo>,</mo>\u0000 <mi>r</mi>\u0000 <mo>&gt;</mo>\u0000 <mfrac>\u0000 <mn>3</mn>\u0000 <mn>2</mn>\u0000 </mfrac>\u0000 </mrow>\u0000 <annotation>$p,q,r&gt;frac{3}{2}$</annotation>\u0000 </semantics></math>. Furthermore, we establish several new blowup criteria in anisotropic Besov spaces with negative indices. These results extend the eigenvalue regularity criteria to a broader class of scale-invariant anisotropic spaces.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 6","pages":"1306-1320"},"PeriodicalIF":0.8,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148160717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Long-Time Solvability and Asymptotics for the 3D Rotating MHD Equations","authors":"Hiroki Ohyama","doi":"10.1002/mana.70152","DOIUrl":"https://doi.org/10.1002/mana.70152","url":null,"abstract":"<p>We consider the initial value problem for the 3D incompressible rotating MHD equations around a constant magnetic field. We prove the long-time existence and uniqueness of solutions for small viscosity coefficient and high rotating speed. Moreover, we investigate the asymptotic behavior of solutions in the limit of vanishing viscosity and fast rotation, and show that the velocity and magnetic field converge to the zero vector and the solution to the linear heat equation, respectively. We also derive the rates of these convergences in some space-time norm.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 6","pages":"1480-1509"},"PeriodicalIF":0.8,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70152","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148160673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Harmonic Vector Fields and Rigidity of Multiply Warped Products","authors":"Sinem Güler,&nbsp;Bülent Ünal","doi":"10.1002/mana.70148","DOIUrl":"https://doi.org/10.1002/mana.70148","url":null,"abstract":"<div>\u0000 \u0000 <p>We investigate harmonic vector fields on multiply warped products in both Riemannian and Lorentzian settings. An explicit decomposition formula for the rough Laplacian acting on vector fields is established, separating horizontal and vertical components and revealing the coupling effects induced by multiple warping functions. This analytic description yields sharp characterizations of harmonicity and leads to strong rigidity phenomena. In particular, we show that, under natural compactness, curvature, and completeness assumptions, the existence of nontrivial harmonic vector fields strongly restricts the warping structure, leading to splitting results and, in the rigid regime, forcing the warping function to obey a specific power-law expansion. Applications include generalized Robertson–Walker and Kasner-type spacetimes, where harmonic vector fields impose strong constraints on anisotropic expansion.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 6","pages":"1373-1397"},"PeriodicalIF":0.8,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148160745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonnegative Radial Solutions of a Weighted Elliptic Problem in Exterior Domains","authors":"Xiaohong Guan,&nbsp;Jiaqi Yao","doi":"10.1002/mana.70145","DOIUrl":"https://doi.org/10.1002/mana.70145","url":null,"abstract":"<div>\u0000 \u0000 <p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <mo>=</mo>\u0000 <mo>{</mo>\u0000 <mi>x</mi>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>N</mi>\u0000 </msup>\u0000 <mspace></mspace>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>≥</mo>\u0000 <mn>3</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>:</mo>\u0000 <mspace></mspace>\u0000 <mo>|</mo>\u0000 <mi>x</mi>\u0000 <mo>|</mo>\u0000 <mo>&lt;</mo>\u0000 <mn>1</mn>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$B=lbrace x in R^N ; (N ge 3): ; |x|&lt;1rbrace$</annotation>\u0000 </semantics></math> be the unit ball in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>N</mi>\u0000 </msup>\u0000 <annotation>$R^N$</annotation>\u0000 </semantics></math>. The structure of nonnegative radial solutions of a weighted elliptic problem in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>N</mi>\u0000 </msup>\u0000 <mrow>\u0000 <mo>∖</mo>\u0000 </mrow>\u0000 <mover>\u0000 <mi>B</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 </mrow>\u0000 <annotation>$R^N backslash {overline{B}}$</annotation>\u0000 </semantics></math> with Neumann or Robin boundary conditions on <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>∂</mi>\u0000 <mi>B</mi>\u0000 </mrow>\u0000 <annotation>$partial B$</annotation>\u0000 </semantics></math> is studied. It is seen that the problem admits a unique positive radial fast-decay solution for the supercritical case and the problem does not admit nontrivial nonnegative radial solution for the critical case. It is expected that the problem does not admit nontrivial nonnegative (radial and non-radial) solutions for the subcritical and critical cases.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 6","pages":"1336-1349"},"PeriodicalIF":0.8,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148160766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometric Properties of Homomorphisms between the Absolute Galois Groups of Mixed-characteristic Complete Discrete Valuation Fields with Perfect Residue Fields","authors":"Takahiro Murotani","doi":"10.1002/mana.70143","DOIUrl":"https://doi.org/10.1002/mana.70143","url":null,"abstract":"<div>\u0000 \u0000 <p>Although the analog of the theorem of Neukirch–Uchida for <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-adic local fields fails to hold as it is, a certain analog of this theorem for the absolute Galois groups with ramification filtrations of <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-adic local fields was proved by Mochizuki. Moreover, various necessary and sufficient conditions for homomorphisms between the absolute Galois groups of <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-adic local fields to be “geometric” (i.e., to arise from homomorphisms of fields) were given by Mochizuki and Hoshi. In this paper, we consider similar problems for general mixed-characteristic complete discrete valuation fields with perfect residue fields and homomorphisms between their absolute Galois groups preserving certain structures related to Hodge–Tate representations. One main result gives necessary and sufficient conditions for homomorphisms between the absolute Galois groups of mixed-characteristic complete discrete valuation fields with residue fields algebraic over the prime fields to be geometric. We also give a “weak-Isom” anabelian result (i.e., a sufficient condition for the existence of an isomorphism between two fields in question) for homomorphisms between the absolute Galois groups of these fields.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 6","pages":"1321-1335"},"PeriodicalIF":0.8,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148160793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Harnack-Type Inequality for a Perturbed Singular Liouville Equation","authors":"Daniele Bartolucci,&nbsp;Paolo Cosentino,&nbsp;Lina Wu","doi":"10.1002/mana.70149","DOIUrl":"https://doi.org/10.1002/mana.70149","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;Motivated by the Onsager statistical mechanics description of turbulent Euler flows with point singularities, we obtain a Harnack-type inequality for sequences of solutions of the following perturbed Liouville equation,\u0000\u0000 &lt;/p&gt;&lt;div&gt;&lt;span&gt;&lt;span&gt;&lt;!--FIGURE--&gt;&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;Δ&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/msup&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;V&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;mstyle&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mstyle&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mtext&gt;in&lt;/mtext&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$begin{equation*} nonumber -Delta v_n={left({epsilon _n^2+|x|^2}right)}^{alpha _n}V_n(x)e^{displaystyle v_n} qquad text{in } ,,, Omega, end{equation*}$$&lt;/annotation","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 6","pages":"1398-1417"},"PeriodicalIF":0.8,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148160746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some Results on Spanned Vector Bundles of Corank 0","authors":"Antonio Lanteri,&nbsp;Andrew J. Sommese","doi":"10.1002/mana.70153","DOIUrl":"https://doi.org/10.1002/mana.70153","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;A class &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathcal {C}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of vector bundles &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathcal {E}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of rank &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;annotation&gt;$N$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; on an &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;annotation&gt;$N$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-dimensional complex projective variety &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, spanned by global sections, with positive top Chern class and ample determinant is investigated. The standard relation between Chern and Segre polynomials allows us to decide about the bigness of a bundle closely related to &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathcal {E}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. The size &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$sigma (X,{mathcal {E}})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, an integer measuring the deviation of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathcal {E}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; from bigness, is introduced and studied. The structure of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathcal {C}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, in connection with the behavior of the size, yields a useful tool to produce several examples. Among them the pair &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(mathbb {P}^N, T_{mathbb {P}^N}(-1))$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; emerges, of which two characterizations are provided in terms of ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 6","pages":"1269-1279"},"PeriodicalIF":0.8,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148160802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Relationship Between Carleson Measures and BMO Spaces Associated With Schrödinger Aq Weights","authors":"Federico Campos,&nbsp;Oscar Salinas,&nbsp;Beatriz Viviani","doi":"10.1002/mana.70150","DOIUrl":"https://doi.org/10.1002/mana.70150","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we consider a Schrödinger operator with a non-negative potential satisfying a reverse Hölder inequality and its associated critical radius function <span></span><math>\u0000 <semantics>\u0000 <mi>ρ</mi>\u0000 <annotation>$rho$</annotation>\u0000 </semantics></math>. Given a weight <span></span><math>\u0000 <semantics>\u0000 <mi>w</mi>\u0000 <annotation>$w$</annotation>\u0000 </semantics></math> in a Muckenhoupt class related to <span></span><math>\u0000 <semantics>\u0000 <mi>ρ</mi>\u0000 <annotation>$rho$</annotation>\u0000 </semantics></math>, we characterize the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <mi>M</mi>\u0000 <msub>\u0000 <mi>O</mi>\u0000 <mrow>\u0000 <mi>ρ</mi>\u0000 <mo>,</mo>\u0000 <mi>w</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$BMO_{rho, w}$</annotation>\u0000 </semantics></math> space with Carleson measures associated to <span></span><math>\u0000 <semantics>\u0000 <mi>w</mi>\u0000 <annotation>$w$</annotation>\u0000 </semantics></math>.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 6","pages":"1418-1445"},"PeriodicalIF":0.8,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148160800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}