Mathematische Nachrichten最新文献

{"title":"Real Noncommutative Convexity. II: Extremality and Noncommutative Convex Functions","authors":"David P. Blecher,&nbsp;Caleb Becker McClure","doi":"10.1002/mana.70135","DOIUrl":"https://doi.org/10.1002/mana.70135","url":null,"abstract":"<div>\u0000 \u0000 <p>We continue the development of real noncommutative (nc) convexity, building on the recent and profound complex theory of Davidson and Kennedy. This paper focuses on the theory of nc extreme points (and pure and maximal points) and the nc Choquet boundary in the real setting, as well as on the theory of real nc convex and semicontinuous functions and real nc convex envelopes. Our main emphasis is on how these notions interact with complexification. In particular, parts of the paper analyze in detail how various notions of “extreme” or “maximal” relate to our earlier concept of the complexification of a convex set. Several new features emerge in the real case, especially in the later sections, including the novel notions of the complexification of an nc convex function and of the complexification of the convex envelope of an nc function. With an Appendix by Russell.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 6","pages":"1280-1305"},"PeriodicalIF":0.8,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148160700","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":"Isoperimetric Inequality With Zero Magnetic Field in Doubly Connected Domains","authors":"Mrityunjoy Ghosh,&nbsp;Ayman Kachmar","doi":"10.1002/mana.70136","DOIUrl":"https://doi.org/10.1002/mana.70136","url":null,"abstract":"<div>\u0000 \u0000 <p>We investigate how the lowest eigenvalue of a magnetic Laplacian depends on the geometry of a planar domain with a disk-shaped hole, where the magnetic field is generated by a singular flux. Under Dirichlet boundary conditions on the inner boundary and Neumann boundary conditions on the outer boundary, we show that this eigenvalue is maximized when the domain is an annulus, for a fixed area and magnetic flux. As consequences, we establish geometric inequalities for eigenvalues in settings with both singular and localized magnetic fields. We also propose a conjecture for a general optimality result and establish its validity for large magnetic fluxes.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 5","pages":"1230-1240"},"PeriodicalIF":0.8,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148061356","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":"Moderate Deviation Principles for Lacunary Trigonometric Sums","authors":"Joscha Prochno,&nbsp;Marta Strzelecka","doi":"10.1002/mana.70126","DOIUrl":"https://doi.org/10.1002/mana.70126","url":null,"abstract":"<p>Classical works of Kac, Salem, and Zygmund, and Erdős and Gál have shown that lacunary trigonometric sums despite their dependency structure behave in various ways like sums of independent and identically distributed random variables. For instance, they satisfy a central limit theorem (CLT) and a law of the iterated logarithm. Those results have only recently been complemented by large deviation principles by Aistleitner, Gantert, Kabluchko, Prochno, and Ramanan, showing that interesting phenomena occur on the large deviation scale that are not visible in the classical works. This raises the question on what scale such phenomena kick in. In this paper, we provide a first step toward a resolution of this question by studying moderate deviation principles for lacunary trigonometric sums. We show that no arithmetic affects are visible between the CLT scaling <span></span><math>\u0000 <semantics>\u0000 <msqrt>\u0000 <mi>n</mi>\u0000 </msqrt>\u0000 <annotation>$sqrt {n}$</annotation>\u0000 </semantics></math> and a scaling <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>/</mo>\u0000 <mi>log</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$n/log (n)$</annotation>\u0000 </semantics></math> that is only a logarithmic gap away from the large deviations scale. To obtain our results, we introduce correlation graphs and use the method of cumulants.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 5","pages":"1028-1044"},"PeriodicalIF":0.8,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70126","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148084251","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":"Smooth Dynamics of a New Semilinear Bresse–Fourier System: A Semigroup Approach","authors":"Irving J. R. Barreto,&nbsp;Marcio A. Jorge Silva,&nbsp;To Fu Ma","doi":"10.1002/mana.70130","DOIUrl":"https://doi.org/10.1002/mana.70130","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper is concerned with a thermoelastic Bresse system that models the dynamics of arched beams. It analyzes the effect of temperature on each constitutive equation, namely the shear force, bending moment, and axial force. Within a framework that uses Fourier's law of heat conduction, the exponential stability of the model is studied. To make the analysis more involved, we consider Dirichlet boundary conditions, which introduce technical challenges in handling the boundary terms. These challenges are addressed using a truncation argument and an observability inequality. In addition, we establish the existence of a smooth global attractor when the system is submitted to a nonlinear foundation. We do not use energy methods. Instead, we explore the uniform stability of the homogeneous problem.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 5","pages":"1125-1139"},"PeriodicalIF":0.8,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148084300","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":"Conformally Flat Minimal Lagrangian Submanifolds in Complex Space Forms With Parallel Ricci Tensor","authors":"Hongru Song,&nbsp;Ruixin Wang,&nbsp;Cheng Xing","doi":"10.1002/mana.70133","DOIUrl":"https://doi.org/10.1002/mana.70133","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we focus on the open problem of classifying <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-dimensional conformally flat minimal Lagrangian submanifolds in complex space forms for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>≥</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$nge 3$</annotation>\u0000 </semantics></math>, motivated by the classification of minimal Lagrangian submanifolds with constant sectional curvature. As the main result, we completely solve the problem by assuming that the Ricci tensor is parallel, with respect to the Levi–Civita connection, which is introduced as a natural extension of the Einstein condition.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 5","pages":"1182-1196"},"PeriodicalIF":0.8,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148092207","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":"Existence, Non-Existence, and Uniqueness of Solutions for a Generalized Fractional p-Kirchhoff Equation","authors":"J. Vanterler da C. Sousa,&nbsp;Romulo Diaz Carlos,&nbsp;El-Houari Hamza","doi":"10.1002/mana.70125","DOIUrl":"https://doi.org/10.1002/mana.70125","url":null,"abstract":"<p>This paper investigates the existence and non-existence and uniqueness of global solutions for certain parameter values <span></span><math>\u0000 <semantics>\u0000 <mi>c</mi>\u0000 <annotation>$c$</annotation>\u0000 </semantics></math> in a new class of generalized fractional <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-Kirchhoff equations in the whole space. Using the Pohozaev and Nehari identities for an auxiliary problem, together with the fractional Gagliardo–Nirenberg inequality and the concentration–compactness principle, we prove that all optimizer solutions to the auxiliary problem are, in fact, unique minimizer solutions to the original problem.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 5","pages":"1004-1027"},"PeriodicalIF":0.8,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70125","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148080546","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":"On Non-Compact Extended Bach Solitons","authors":"Rahul Poddar","doi":"10.1002/mana.70131","DOIUrl":"https://doi.org/10.1002/mana.70131","url":null,"abstract":"<p>We study the characterization of non-compact solitons of the extended Bach flow, known as an extended Bach soliton. We prove that a weakly conformally flat extended Bach soliton <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>M</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>,</mo>\u0000 <mi>g</mi>\u0000 <mo>,</mo>\u0000 <mi>V</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(M^n,g,V)$</annotation>\u0000 </semantics></math> with harmonic Weyl tensor is Bach-flat and the potential vector field <span></span><math>\u0000 <semantics>\u0000 <mi>V</mi>\u0000 <annotation>$V$</annotation>\u0000 </semantics></math> is conformal. In the case of an extended gradient Bach soliton, we impose certain regularity conditions on the potential function, Ricci curvature constraints on <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>, and assume that the Weyl tensor is harmonic, to deduce that <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> is trivial and Bach-flat.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 5","pages":"1140-1151"},"PeriodicalIF":0.8,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70131","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148084301","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":"A Minimum Problem Associated With Scalar Ginzburg–Landau Equation and Free Boundary","authors":"Yuwei Hu,&nbsp;Jun Zheng,&nbsp;Leandro S. Tavares","doi":"10.1002/mana.70134","DOIUrl":"https://doi.org/10.1002/mana.70134","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;Let &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;/mrow&gt;\u0000 &lt;annotation&gt;$Nge 2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/mrow&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;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$pin left(frac{2N}{N+2},+infty right)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;annotation&gt;$Omega$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be an open bounded domain in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&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;annotation&gt;$mathbb {R}^N$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with smooth boundary. We consider the minimum problem &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mo&gt;∫&lt;/mo&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mo&gt;∇&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msup&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mn&gt;1&lt;/mn&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;msup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 5","pages":"1197-1229"},"PeriodicalIF":0.8,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148093262","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":"H-Points and H-Property of the Orlicz Spaces Endowed With the s-Norms","authors":"Serap Öztop,&nbsp;Badik Hüseyin Uysal","doi":"10.1002/mana.70128","DOIUrl":"https://doi.org/10.1002/mana.70128","url":null,"abstract":"<p>In this paper, we investigate the set of H-points on the unit sphere of the Orlicz spaces over non-atomic and purely atomic measure spaces. Building upon these arguments, we establish a criteria for the H-property in Orlicz spaces. In addition, our results yield several consequences related to the geometric properties of the Orlicz spaces, particularly concerning extreme points, strongly extreme points, strictly convex, midpoint locally uniformly convex, denting points and G-property. This study unifies and extends previous results obtained for the Orlicz and Luxemburg norms and fills a gap in the literature concerning the <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-Amemiya norms.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 5","pages":"1062-1084"},"PeriodicalIF":0.8,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70128","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148097968","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":"Existence of Solutions for a Singular m-Triharmonic Equation With Logarithmic Nonlinearity","authors":"Ayşe Fidan,&nbsp;Erhan Pişkin","doi":"10.1002/mana.70123","DOIUrl":"https://doi.org/10.1002/mana.70123","url":null,"abstract":"<div>\u0000 \u0000 <p>In this work, we study the singular <span></span><math>\u0000 <semantics>\u0000 <mi>m</mi>\u0000 <annotation>$ m$</annotation>\u0000 </semantics></math> -triharmonic equation with logarithmic nonlinearity. We establish the local existence by the existence by the technique of cut-off combining with the Faedo–Galerkin approximation. Based on the potential well method, the global existence of the weak solution is derived.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 5","pages":"985-1003"},"PeriodicalIF":0.8,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148100022","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}