Mathematische Nachrichten最新文献

{"title":"On rank 3 quadratic equations of Veronese embeddings","authors":"Euisung Park,&nbsp;Saerom Sim","doi":"10.1002/mana.70028","DOIUrl":"https://doi.org/10.1002/mana.70028","url":null,"abstract":"<p>This paper studies the geometric structure of the locus <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>Φ</mi>\u0000 <mn>3</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$Phi _3 (X)$</annotation>\u0000 </semantics></math> of rank 3 quadratic equations of the Veronese variety <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mi>ν</mi>\u0000 <mi>d</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$X = nu _d ({mathbb {P}}^n)$</annotation>\u0000 </semantics></math>. Specifically, we investigate the minimal irreducible decomposition of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>Φ</mi>\u0000 <mn>3</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$Phi _3 (X)$</annotation>\u0000 </semantics></math> of rank 3 quadratic equations and analyze the geometric properties of the irreducible components of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>Φ</mi>\u0000 <mn>3</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$Phi _3 (X)$</annotation>\u0000 </semantics></math> such as their desingularizations. Additionally, we explore the non-singularity and singularity of these irreducible components of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>Φ</mi>\u0000 <mn>3</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$Phi _3 (X)$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 9","pages":"3135-3155"},"PeriodicalIF":0.8,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037578","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":"On the index of Fraser–Sargent-type minimal surfaces","authors":"Vladimir Medvedev,&nbsp;Egor Morozov","doi":"10.1002/mana.12035","DOIUrl":"https://doi.org/10.1002/mana.12035","url":null,"abstract":"<p>Fraser–Sargent surfaces are free boundary minimal surfaces in the four-dimensional unit Euclidean ball. Extended infinitely they define immersed minimal surfaces in the Euclidean space. The parts of these surfaces outside the ball are exterior-free boundary minimal surfaces. We prove that they are stable. Independently of it, we find an upper bound on the index of Fraser–Sargent surfaces inside the ball. Also, we provide computational experiments and state a conjecture about an improved index lower bound of the orientable cover of Fraser–Sargent surfaces inside the ball. Finally, based on a similar computational experiment for infinitely extended Fraser–Sargent surfaces, we state a conjecture about their index.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 9","pages":"3007-3026"},"PeriodicalIF":0.8,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037605","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":"Cosmic no-hair conjecture and conformal vector fields","authors":"Seungsu Hwang,&nbsp;Gabjin Yun","doi":"10.1002/mana.70025","DOIUrl":"https://doi.org/10.1002/mana.70025","url":null,"abstract":"&lt;p&gt;In this paper, we investigate cosmic no-hair properties mathematically when a given Riemannian manifold admits a nontrivial closed conformal vector field. Let &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;M&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(M^n, g)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a compact Riemannian &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;-manifold with connected non-empty boundary &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$partial M$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Assume that there exists a smooth function &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;annotation&gt;$f$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;annotation&gt;$M$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$f&gt;0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mo&gt;∖&lt;/mo&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$M setminus partial M$&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;mrow&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$partial M = f^{-1}(0)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; satisfying the static vacuum equation. We prove that if &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;M&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(M^n, g)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 9","pages":"3061-3074"},"PeriodicalIF":0.8,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145038577","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":"Real hypersurfaces of \u0000 \u0000 \u0000 \u0000 S\u0000 2\u0000 \u0000 ×\u0000 \u0000 S\u0000 2\u0000 \u0000 \u0000 $mathbb {S}^2times mathbb {S}^2$\u0000 and \u0000 \u0000 \u0000 \u0000 H\u0000 2\u0000 \u0000 ×\u0000 \u0000 H\u0000 2\u0000 \u0000 \u0000 $mathbb {H}^2times mathbb {H}^2$\u0000 with parallel operators","authors":"Zejun Hu,&nbsp;Xiaoge Lu","doi":"10.1002/mana.70024","DOIUrl":"https://doi.org/10.1002/mana.70024","url":null,"abstract":"<p>On real hypersurafces of the Kähler surface <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbb {S}^2times mathbb {S}^2$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbb {H}^2times mathbb {H}^2$</annotation>\u0000 </semantics></math>, there are three typical operators: the shape operator, the structure Lie operator, and the contact Lie operator. In this paper, we study real hypersurfaces in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbb {S}^2times mathbb {S}^2$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbb {H}^2times mathbb {H}^2$</annotation>\u0000 </semantics></math> related to these operators. As the main results, we classify real hypersurfaces of both <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbb {S}^2times mathbb {S}^2$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbb {H}^2times mathbb {H}^2$</annotation>\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2888-2900"},"PeriodicalIF":0.8,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144832977","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":"Heisenberg-smooth operators from the phase-space perspective","authors":"Robert Fulsche,&nbsp;Lauritz van Luijk","doi":"10.1002/mana.70019","DOIUrl":"https://doi.org/10.1002/mana.70019","url":null,"abstract":"<p>Cordes' characterization of Heisenberg-smooth operators bridges a gap between the theory of pseudo-differential operators and quantum harmonic analysis (QHA). We give a new proof of the result by using the phase-space formalism of QHA. Our argument is flexible enough to generalize Cordes' result in several directions: (1) we can admit general quantization schemes, (2) allow for other phase-space geometries, (3) obtain Schatten-class analogs of the result, and (4) are able to characterize precisely ‘Heisenberg-analytic’ operators. For (3), we use QHA to derive Schatten versions of the Calderón–Vaillancourt theorem, which might be of independent interest.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2845-2866"},"PeriodicalIF":0.8,"publicationDate":"2025-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144833292","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":"Approximation of Dirac operators with \u0000 \u0000 δ\u0000 ${delta }$\u0000 -shell potentials in the norm resolvent sense. I. Qualitative results","authors":"Jussi Behrndt,&nbsp;Markus Holzmann,&nbsp;Christian Stelzer-Landauer","doi":"10.1002/mana.70004","DOIUrl":"https://doi.org/10.1002/mana.70004","url":null,"abstract":"<p>In this paper, the approximation of Dirac operators with general <span></span><math>\u0000 <semantics>\u0000 <mi>δ</mi>\u0000 <annotation>$delta$</annotation>\u0000 </semantics></math>-shell potentials supported on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$C^2$</annotation>\u0000 </semantics></math>-curves in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$mathbb {R}^2$</annotation>\u0000 </semantics></math> or <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$C^2$</annotation>\u0000 </semantics></math>-surfaces in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>$mathbb {R}^3$</annotation>\u0000 </semantics></math>, which may be bounded or unbounded, is studied. It is shown under suitable conditions on the weight of the <span></span><math>\u0000 <semantics>\u0000 <mi>δ</mi>\u0000 <annotation>$delta$</annotation>\u0000 </semantics></math>-interaction that a family of Dirac operators with regular, squeezed potentials converges in the norm resolvent sense to the Dirac operator with the <span></span><math>\u0000 <semantics>\u0000 <mi>δ</mi>\u0000 <annotation>$delta$</annotation>\u0000 </semantics></math>-shell interaction.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2499-2546"},"PeriodicalIF":0.8,"publicationDate":"2025-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144833293","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":"Uniform (d+1)-bundle over the Grassmannian G(d,n) in positive characteristics","authors":"Rong Du,&nbsp;Yuhang Zhou","doi":"10.1002/mana.70022","DOIUrl":"https://doi.org/10.1002/mana.70022","url":null,"abstract":"<p>This paper is dedicated to the classification of uniform vector bundles of rank <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$d+1$</annotation>\u0000 </semantics></math> over the Grassmannian <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <mo>(</mo>\u0000 <mi>d</mi>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$G(d,n)$</annotation>\u0000 </semantics></math> (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mo>≤</mo>\u0000 <mi>d</mi>\u0000 <mo>≤</mo>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 <annotation>$2le dle n-d$</annotation>\u0000 </semantics></math>) over an algebraically closed field in positive characteristics. Specifically, we show that all uniform vector bundles with rank <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$d+1$</annotation>\u0000 </semantics></math> over <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <mo>(</mo>\u0000 <mi>d</mi>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$G(d,n)$</annotation>\u0000 </semantics></math> are homogeneous.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2867-2887"},"PeriodicalIF":0.8,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144833355","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":"Asymptotic analysis of the Navier–Stokes equations in a thin domain with power-law slip boundary conditions","authors":"María Anguiano,&nbsp;Francisco J. Suárez-Grau","doi":"10.1002/mana.70011","DOIUrl":"https://doi.org/10.1002/mana.70011","url":null,"abstract":"&lt;p&gt;This theoretical study deals with the Navier–Stokes equations posed in a 3D thin domain with thickness &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mo&gt;≪&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$0&lt;varepsilon ll 1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, assuming power-law slip boundary conditions, with an anisotropic tensor, on the bottom. This condition, introduced in (Djoko et al. &lt;i&gt;Comput. Math. Appl&lt;/i&gt;. &lt;b&gt;128&lt;/b&gt; (2022) 198–213), represents a generalization of the Navier slip boundary condition. The goal is to study the influence of the power-law slip boundary conditions with an anisotropic tensor of order &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mi&gt;γ&lt;/mi&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$varepsilon ^{gamma over s}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;γ&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$gamma in mathbb {R}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and flow index &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&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;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$1&lt;s&lt;2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, on the behavior of the fluid with thickness &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;annotation&gt;$varepsilon$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; by using asymptotic analysis when &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$varepsilon rightarrow 0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, depending on the values of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;γ&lt;/mi&gt;\u0000 &lt;annotation&gt;$gamma$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. As a result, we deduce the existence of a critical value of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;γ&lt;/mi&gt;\u0000 &lt;annotation&gt;$gamma$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; given by &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;γ&lt;/mi&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;∗&lt;/mo&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2691-2711"},"PeriodicalIF":0.8,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144833282","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":"Singular integrals associated with Zygmund dilations on multiparameter weighted Hardy spaces","authors":"Jian Tan","doi":"10.1002/mana.70016","DOIUrl":"https://doi.org/10.1002/mana.70016","url":null,"abstract":"<p>The aim of this paper is to establish the boundedness of multiparameter singular integral operators associated with Zygmund dilations on product weighted Hardy spaces in the three-parameter setting. Additionally, we show that this class of operators are bounded on product Hardy spaces associated with ball quasi-Banach function spaces by employing the Rubio de Francia extrapolation technique. The generality of our result is illustrated by their applicability to concrete function spaces such as product Herz spaces and weighted product Morrey spaces. Even in these specific cases, the application yields entirely new results.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2794-2813"},"PeriodicalIF":0.8,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144833283","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":"Uniform stability of the inverse problem for the non-self-adjoint Sturm–Liouville operator","authors":"Natalia P. Bondarenko","doi":"10.1002/mana.70018","DOIUrl":"https://doi.org/10.1002/mana.70018","url":null,"abstract":"<p>In this paper, we develop a new approach to investigation of the uniform stability for inverse spectral problems. We consider the non-self-adjoint Sturm–Liouville problem that consists in the recovery of the potential and the parameters of the boundary conditions from the eigenvalues and the generalized weight numbers. The special case of simple eigenvalues, as well as the general case with multiple eigenvalues, is studied. We find various subsets in the space of spectral data, on which the inverse mapping is Lipschitz continuous, and obtain the corresponding unconditional uniform stability estimates. Furthermore, the conditional uniform stability of the inverse problem under a priori restrictions on the potential is studied. In addition, we prove the uniform stability of the inverse problem by the Cauchy data, which are convenient for numerical reconstruction of the potential and for applications to partial inverse problems.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2814-2844"},"PeriodicalIF":0.8,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144833012","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}