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Monotone properties of the second even Neumann eigenfunction in symmetric domains 对称域上第二偶Neumann本征函数的单调性
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2025-09-27 DOI: 10.1007/s10231-025-01615-7
Hongbin Chen, Ke Wu, Ruofei Yao
{"title":"Monotone properties of the second even Neumann eigenfunction in symmetric domains","authors":"Hongbin Chen,&nbsp;Ke Wu,&nbsp;Ruofei Yao","doi":"10.1007/s10231-025-01615-7","DOIUrl":"10.1007/s10231-025-01615-7","url":null,"abstract":"<div><p>This paper investigates symmetric Neumann eigenfunctions on a class of planar domains that possess a single line of symmetry. We focus on the Neumann eigenfunctions corresponding to the second eigenvalue among functions that are symmetric with respect to the axis of symmetry of the domain. By employing the method of continuity, we establish the monotonicity of these eigenfunctions in the direction parallel to the axis of symmetry. Furthermore, we show that the corresponding eigenfunction is a Morse function on the boundary with exactly two critical points, and that the associated eigenvalue is simple within the space of symmetric functions.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 2","pages":"635 - 657"},"PeriodicalIF":0.9,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147828600","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}
引用次数: 0
Transfinite hypercentral iterated wreath product of integral domains 积分域的超限超中心迭代环积
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2025-09-26 DOI: 10.1007/s10231-025-01616-6
Riccardo Aragona, Norberto Gavioli, Giuseppe Nozzi
{"title":"Transfinite hypercentral iterated wreath product of integral domains","authors":"Riccardo Aragona,&nbsp;Norberto Gavioli,&nbsp;Giuseppe Nozzi","doi":"10.1007/s10231-025-01616-6","DOIUrl":"10.1007/s10231-025-01616-6","url":null,"abstract":"<div><p>Starting with an integral domain <i>D</i> of characteristic 0, we consider a class of iterated wreath product <span>(W_n)</span> of <i>n</i> copies of <i>D</i>. In order that <span>(W_n)</span> be transfinite hypercentral, it is necessary to restrict to the case of wreath products defined by way of numerical polynomials. We also associate to each of these groups a Lie ring, providing a correspondence preserving most of the structure. This construction generalizes a result of Sushchansky and Netreba (Algebra Discrete Math 122–132, 2005) which characterizes the Lie algebras associated to the Sylow <span>(p)</span>-subgroups of the symmetric group <span>({{,textrm{Sym},}}(p^n))</span>. As an application, we explore the normalizer chain <span>(lbrace textbf{N}_{i}rbrace _{ige -1})</span> starting from the canonical regular abelian subgroup <i>T</i> of <span>(W_n)</span>. Finally, we characterize the regular abelian normal subgroups of <span>(textbf{N}_0)</span> that are isomorphic to <span>(D^n)</span>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 2","pages":"659 - 682"},"PeriodicalIF":0.9,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-025-01616-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147828545","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}
引用次数: 0
On extension of closed complex (basic) differential forms: (basic) Hodge numbers and (transversely) p-Kähler structures 闭复（基本）微分形式的扩展：（基本）霍奇数和（横向）p-Kähler结构
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2025-09-24 DOI: 10.1007/s10231-025-01610-y
Sheng Rao, Runze Zhang
{"title":"On extension of closed complex (basic) differential forms: (basic) Hodge numbers and (transversely) p-Kähler structures","authors":"Sheng Rao,&nbsp;Runze Zhang","doi":"10.1007/s10231-025-01610-y","DOIUrl":"10.1007/s10231-025-01610-y","url":null,"abstract":"<div><p>Inspired by a recent work of Wei–Zhu on the extension of closed complex differential forms and Voisin’s usage of the <span>(partial overline{partial })</span>-lemma, we obtain several new theorems of deformation invariance of Hodge numbers and reprove the local stabilities of <i>p</i>-Kähler structures with the <span>(partial overline{partial })</span>-property. Our approach is more concerned with the <i>d</i>-closed extension by means of the exponential operator <span>(e^{iota _varphi })</span>. Furthermore, we prove the local stabilities of transversely <i>p</i>-Kähler structures with mild <span>(partial overline{partial })</span>-property by adapting the power series method to the foliated case, which strengthens the works of El Kacimi Alaoui–Gmira and Raźny on that of the transversely Kähler foliations with homologically orientability. We observe that a transversely Kähler foliation, even without homologically orientability, also satisfies the <span>(partial overline{partial })</span>-property. So even when <span>(p=1)</span> (transversely Kähler), our results are new as we can drop the assumption in question on the initial foliation. Several theorems on the deformation invariance of basic Hodge/Bott–Chern numbers with mild <span>(partial overline{partial })</span>-properties are also presented.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 1","pages":"425 - 482"},"PeriodicalIF":0.9,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579244","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}
引用次数: 0
On the second-order regularity of solutions to widely singular or degenerate elliptic equations 广义奇异或退化椭圆型方程解的二阶正则性
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2025-09-16 DOI: 10.1007/s10231-025-01607-7
Pasquale Ambrosio, Antonio Giuseppe Grimaldi, Antonia Passarelli di Napoli
{"title":"On the second-order regularity of solutions to widely singular or degenerate elliptic equations","authors":"Pasquale Ambrosio,&nbsp;Antonio Giuseppe Grimaldi,&nbsp;Antonia Passarelli di Napoli","doi":"10.1007/s10231-025-01607-7","DOIUrl":"10.1007/s10231-025-01607-7","url":null,"abstract":"<div><p>We consider local weak solutions to PDEs of the type </p><div><div><span>$$ -,textrm{div}left( (vert Duvert -lambda )_{+}^{p-1}frac{Du}{vert Duvert }right) =f,,,,,,,text {in},,Omega , $$</span></div></div><p>where <span>(1&lt;p&lt;infty )</span>, <span>(Omega )</span> is an open subset of <span>(mathbb {R}^{n})</span> for <span>(nge 2)</span>, <span>(lambda )</span> is a positive constant and <span>((,cdot ,)_{+})</span> stands for the positive part. Equations of this form are widely degenerate for <span>(pge 2)</span> and widely singular for <span>(1&lt;p&lt;2)</span>. We establish higher differentiability results for a suitable nonlinear function of the gradient <i>Du</i> of the local weak solutions, assuming that <i>f</i> belongs to the local Besov space <span>(B^{(p-2)/p}_{p',1,loc}(Omega ))</span> when <span>(p&gt;2)</span>, and that <span>(fin L_{loc}^{{frac{np}{n(p-1)+2-p}}}(Omega ))</span> if <span>(1&lt;ple 2)</span>. The conditions on the datum <i>f</i> are essentially sharp. As a consequence, we obtain the local higher integrability of <i>Du</i> under the same minimal assumptions on <i>f</i>. For <span>(lambda =0)</span>, our results give back those contained in Clop et al. (Bull Math Sci 13(12):2350008, 2023) and Irving and Koch (Adv Nonlinear Anal 12(1):20230110, 2023).</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 1","pages":"327 - 364"},"PeriodicalIF":0.9,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-025-01607-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579234","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}
引用次数: 0
Dynamical behaviour of a soap film bridge driven by an electrostatic force 静电驱动下皂膜桥的动力特性
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2025-09-12 DOI: 10.1007/s10231-025-01608-6
Lina Sophie Schmitz
{"title":"Dynamical behaviour of a soap film bridge driven by an electrostatic force","authors":"Lina Sophie Schmitz","doi":"10.1007/s10231-025-01608-6","DOIUrl":"10.1007/s10231-025-01608-6","url":null,"abstract":"<div><p>We study a free boundary problem describing a tubular soap film bridge driven by an electrostatic force. To realize the electrostatic force, the soap film bridge is placed inside an outer metal cylinder and a voltage difference between this cylinder and the soap film is applied. Our model consists of a quasilinear parabolic equation for the evolution of the film coupled with an elliptic equation for the electrostatic potential in the unknown domain between outer cylinder and soap film bridge. For the rotationally symmetric case, we prove local well-posedness of this free boundary problem by recasting it as a single quasilinear parabolic equation with a non-local source term. Moreover, for large applied voltages, we show that solutions do not exist globally for a wide class of initial values.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 1","pages":"365 - 407"},"PeriodicalIF":0.9,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579507","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}
引用次数: 0
Best bounds for the dual Hardy operator minus identity on decreasing functions 对偶Hardy算子在递减函数上减恒等的最佳界
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2025-09-08 DOI: 10.1007/s10231-025-01606-8
Achraf Ben Said, Gord Sinnamon
{"title":"Best bounds for the dual Hardy operator minus identity on decreasing functions","authors":"Achraf Ben Said,&nbsp;Gord Sinnamon","doi":"10.1007/s10231-025-01606-8","DOIUrl":"10.1007/s10231-025-01606-8","url":null,"abstract":"<div><p>The distance from the identity operator <i>I</i> to <span>(H^*)</span>, the dual of the Hardy averaging operator, is studied on the cone of nonnegative, nonincreasing functions in Lebesgue space. The exact value is obtained. Optimal lower bounds are also given for difference, <span>(H^*-I)</span>, of these two operators acting on the same cone. A positive answer is given to a conjecture made in “The norm of Hardy-type oscillation operators in the discrete and continuous settings” by A. Ben Said, S. Boza, and J. Soria. Preprint, 2024. In addition, a direct comparison, with optimal constants, is given between the operators <span>(H-I)</span> and <span>(H^*-I)</span> acting on the cone.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 1","pages":"313 - 325"},"PeriodicalIF":0.9,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579302","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}
引用次数: 0
On the instability of syzygy bundles on toric surfaces 关于环面上合胞束的不稳定性
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2025-09-06 DOI: 10.1007/s10231-025-01604-w
Lucie Devey, Milena Hering, Katharina Jochemko, Hendrik Süß
{"title":"On the instability of syzygy bundles on toric surfaces","authors":"Lucie Devey,&nbsp;Milena Hering,&nbsp;Katharina Jochemko,&nbsp;Hendrik Süß","doi":"10.1007/s10231-025-01604-w","DOIUrl":"10.1007/s10231-025-01604-w","url":null,"abstract":"<div><p>We show that for every toric surface <i>X</i> apart from <span>(mathbb {P}^2)</span> and <span>(mathbb {P}^1times mathbb {P}^1)</span> and every ample line bundle <span>(mathcal {L})</span> on <i>X</i> there exists an ample polarisation <i>A</i> for <i>X</i>, such that the syzygy bundle <span>(M_{mathcal {L}^{otimes d}})</span> associated to the tensor power <span>(mathcal {L}^{otimes d})</span> is not stable with respect to <i>A</i> for every <i>d</i> sufficiently large.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 1","pages":"287 - 293"},"PeriodicalIF":0.9,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-025-01604-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579160","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}
引用次数: 0
Hypersurfaces of any homogeneous ({mathbb {C}P}^3) 任何齐次的超曲面 ({mathbb {C}P}^3)
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2025-08-26 DOI: 10.1007/s10231-025-01605-9
Michaël Liefsoens
{"title":"Hypersurfaces of any homogeneous ({mathbb {C}P}^3)","authors":"Michaël Liefsoens","doi":"10.1007/s10231-025-01605-9","DOIUrl":"10.1007/s10231-025-01605-9","url":null,"abstract":"<div><p>Hypersurfaces are studied and classified under multiple additional assumptions in any Riemannian homogeneous space <span>(({mathbb {C}P}^3, g_a))</span>, including nearly Kähler <span>({mathbb {C}P}^3)</span>. Notably, all extrinsically homogeneous hypersurfaces are classified in all these spaces, with an explicit family of examples. Moreover, for nearly Kähler <span>({mathbb {C}P}^3)</span>, all Hopf hypersurfaces are classified. Finally, Codazzi-like hypersurfaces (and in particular parallel and totally geodesic hypersurfaces), totally umbilical hypersurfaces and constant sectional curvature hypersurfaces are proven to not exist in any homogeneous <span>({mathbb {C}P}^3)</span>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 1","pages":"295 - 311"},"PeriodicalIF":0.9,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579317","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}
引用次数: 0
Fredholm maps of index zero between real Banach manifolds from the viewpoint of covering spaces 从覆盖空间的观点看实巴拿赫流形之间索引零的Fredholm映射
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2025-08-23 DOI: 10.1007/s10231-025-01598-5
Pierluigi Benevieri, Alessandro Calamai, Massimo Furi, Maria Patrizia Pera
{"title":"Fredholm maps of index zero between real Banach manifolds from the viewpoint of covering spaces","authors":"Pierluigi Benevieri,&nbsp;Alessandro Calamai,&nbsp;Massimo Furi,&nbsp;Maria Patrizia Pera","doi":"10.1007/s10231-025-01598-5","DOIUrl":"10.1007/s10231-025-01598-5","url":null,"abstract":"<div><p>We give an exhaustive presentation of the concept of topological orientation for Fredholm maps of index zero between real Banach manifolds introduced by the first and third authors during the last three years of the twentieth century. An application of this orientation to the construction of the degree introduced by the same two authors will be given at the end of the paper.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 1","pages":"119 - 146"},"PeriodicalIF":0.9,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-025-01598-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579237","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}
引用次数: 0
Determination of the number of outer Galois points for any plane curve 确定任意平面曲线的外伽罗瓦点的数目
IF 0.9 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2025-08-21 DOI: 10.1007/s10231-025-01603-x
Satoru Fukasawa, Takeshi Takahashi
{"title":"Determination of the number of outer Galois points for any plane curve","authors":"Satoru Fukasawa,&nbsp;Takeshi Takahashi","doi":"10.1007/s10231-025-01603-x","DOIUrl":"10.1007/s10231-025-01603-x","url":null,"abstract":"<div><p>This paper determines the number of outer Galois points for any plane curve in the remaining open cases. Combined with the results so far, this paper indicates that the following conjecture of Yoshihara holds true: The maximal number of outer Galois points is three.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 1","pages":"281 - 286"},"PeriodicalIF":0.9,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579541","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}
引用次数: 0
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