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On the nonexistence of a Green functor with values (hbox {spin}^c) bordism and spin bordism 值为(hbox {spin}^c)和自旋的Green函子的不存在性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-29 DOI: 10.1007/s00013-026-02229-y
Hassan H. Abdallah, Zachary Halladay, Yigal Kamel
{"title":"On the nonexistence of a Green functor with values (hbox {spin}^c) bordism and spin bordism","authors":"Hassan H. Abdallah,&nbsp;Zachary Halladay,&nbsp;Yigal Kamel","doi":"10.1007/s00013-026-02229-y","DOIUrl":"10.1007/s00013-026-02229-y","url":null,"abstract":"<div><p>We show that there does not exist a <span>(C_2)</span>-ring spectrum whose underlying ring spectrum is <span>(textrm{MSpin}^c)</span> and whose <span>(C_2)</span>-fixed point spectrum is <span>(textrm{MSpin})</span>. As a corollary, the <span>(hbox {spin}^c)</span> and spin orientations of Atiyah–Bott–Shapiro cannot be obtained as the underlying and fixed point maps of a single map of <span>(C_2)</span>-ring spectra.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"377 - 381"},"PeriodicalIF":0.5,"publicationDate":"2026-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-026-02229-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A Liouville-type theorem for subharmonic functions and its applications to quasi-Einstein manifolds 次调和函数的liouville型定理及其在拟爱因斯坦流形中的应用
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-25 DOI: 10.1007/s00013-026-02231-4
Rahul Poddar
{"title":"A Liouville-type theorem for subharmonic functions and its applications to quasi-Einstein manifolds","authors":"Rahul Poddar","doi":"10.1007/s00013-026-02231-4","DOIUrl":"10.1007/s00013-026-02231-4","url":null,"abstract":"<div><p>We prove a Liouville-type theorem for subharmonic functions by assuming a finite weighted Dirichlet integral condition, and then apply it to study the rigidity of complete, non-compact <i>m</i>-quasi-Einstein manifolds. Further, we obtain the triviality of a complete, non-compact <i>m</i>-quasi-Einstein manifold <i>M</i> by imposing certain regularity conditions on the potential function and Ricci curvature constraints on <i>M</i>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"433 - 441"},"PeriodicalIF":0.5,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Complete quasi-Yamabe gradient solitons with bounded scalar curvature 具有有界标量曲率的完全拟雅贝梯度孤子
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-24 DOI: 10.1007/s00013-026-02236-z
Shun Maeta
{"title":"Complete quasi-Yamabe gradient solitons with bounded scalar curvature","authors":"Shun Maeta","doi":"10.1007/s00013-026-02236-z","DOIUrl":"10.1007/s00013-026-02236-z","url":null,"abstract":"<div><p>In this paper, we study complete, nontrivial quasi-Yamabe gradient solitons and obtain partial classification results under natural scalar curvature bounds. Assuming that the scalar curvature is bounded from below or above by the soliton constant, we reduce the problem to a one-dimensional ordinary differential equation and derive several rigidity results. For shrinking and steady solitons with scalar curvature strictly larger than the soliton constant and a positive coefficient of the gradient term, we prove rotational symmetry, whereas for expanding and steady solitons with scalar curvature strictly smaller than the soliton constant and a negative coefficient, we obtain explicit warped-product models whose behavior at infinity is completely determined.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"443 - 451"},"PeriodicalIF":0.5,"publicationDate":"2026-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 commutativity of the Berezin transform 关于Berezin变换的交换性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-23 DOI: 10.1007/s00013-026-02222-5
Alexander Borichev, Gérard Fantolini, El-Hassan Youssfi
{"title":"On the commutativity of the Berezin transform","authors":"Alexander Borichev,&nbsp;Gérard Fantolini,&nbsp;El-Hassan Youssfi","doi":"10.1007/s00013-026-02222-5","DOIUrl":"10.1007/s00013-026-02222-5","url":null,"abstract":"<div><p>We consider the commutativity problem for the Berezin transform on weighted Fock spaces. Given a real number <span>(m&gt;0)</span>, for every <span>(alpha &gt;0)</span>, we denote by <span>(B_{alpha })</span> the Berezin transform associated to the measure <span>(mu _{alpha ,m})</span> with density proportional to <span>(e^{-alpha |z|^m})</span> with respect to the Lebesgue measure on the complex plane and normalized so that <span>(mu _{alpha ,m})</span>. We show that the commutativity relation <span>(B_{alpha }B_{beta }f=B_{beta }B_{alpha }f)</span> holds for all <span>(fin L^{infty }(mathbb {C}))</span> and <span>(alpha ,beta &gt; 0)</span> if and only if <span>(m=2)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"397 - 405"},"PeriodicalIF":0.5,"publicationDate":"2026-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Asymptotics of the shifted finite differences of the overpartition function and a problem of Wang–Xie–Zhang 过配分函数的位移有限差分的渐近性及王协章问题
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-17 DOI: 10.1007/s00013-025-02219-6
Gargi Mukherjee
{"title":"Asymptotics of the shifted finite differences of the overpartition function and a problem of Wang–Xie–Zhang","authors":"Gargi Mukherjee","doi":"10.1007/s00013-025-02219-6","DOIUrl":"10.1007/s00013-025-02219-6","url":null,"abstract":"<div><p>Let <span>(overline{p}(n))</span> denote the overpartition function, and for <span>(jin mathbb {N})</span>, <span>(Delta ^r_j)</span> denote the <i>r</i>-fold applications of the shifted difference operator <span>(Delta _j)</span> defined by <span>(Delta _j(a)(n):=a(n)-a(n-j))</span>. The main goal of this paper is to derive an asymptotic expansion of <span>(Delta ^r_j(overline{p})(n))</span> with an effective error bound which subsequently gives an answer to a problem of Wang, Xie, and Zhang. In order to get the asymptotics of <span>(Delta ^r_j(overline{p})(n))</span>, we derive an asymptotic expansion of the shifted overpartition function <span>(overline{p}(n+k))</span> for any integer <span>(kne 0)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"383 - 396"},"PeriodicalIF":0.5,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A comparison of the regularity of certain classes of monomial ideals and their integral closure 单项式理想若干类的正则性及其整体闭包的比较
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-14 DOI: 10.1007/s00013-026-02225-2
Omkar Javadekar
{"title":"A comparison of the regularity of certain classes of monomial ideals and their integral closure","authors":"Omkar Javadekar","doi":"10.1007/s00013-026-02225-2","DOIUrl":"10.1007/s00013-026-02225-2","url":null,"abstract":"<div><p>Let <span>(S = textsf{k}[x_1, ldots , x_n])</span>, <i>I</i> be an ideal of <i>S</i>, and <span>(bar{I})</span> denote its integral closure. A conjecture of Küronya and Pintye states that for any homogeneous ideal <i>I</i> of <i>S</i>, the inequality <span>(operatorname {reg}(bar{I}) le operatorname {reg}(I))</span> holds, where <span>(operatorname {reg}(_))</span> denotes the Castelnuovo–Mumford regularity. In this article, we prove the conjecture for certain classes of monomial ideals.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"351 - 363"},"PeriodicalIF":0.5,"publicationDate":"2026-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Sharp bounds for the growth and distortion of the analytic part of convex K-quasiconformal harmonic mappings 凸k -拟共形调和映射解析部分的生长和畸变的尖锐界
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-14 DOI: 10.1007/s00013-026-02227-0
Peijin Li, Saminathan Ponnusamy
{"title":"Sharp bounds for the growth and distortion of the analytic part of convex K-quasiconformal harmonic mappings","authors":"Peijin Li,&nbsp;Saminathan Ponnusamy","doi":"10.1007/s00013-026-02227-0","DOIUrl":"10.1007/s00013-026-02227-0","url":null,"abstract":"<div><p>The main aim of this paper is to obtain the sharp upper and lower bounds for the growth and distortion of the analytic part <i>h</i> of sense-preserving convex <i>K</i>-quasiconformal harmonic mappings.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"407 - 416"},"PeriodicalIF":0.5,"publicationDate":"2026-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Double ergodicity of strong horseshoe maps 强马蹄形地图的双遍历性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-06 DOI: 10.1007/s00013-026-02221-6
Aliasghar Sarizadeh
{"title":"Double ergodicity of strong horseshoe maps","authors":"Aliasghar Sarizadeh","doi":"10.1007/s00013-026-02221-6","DOIUrl":"10.1007/s00013-026-02221-6","url":null,"abstract":"<div><p>In this paper, we investigate the double ergodicity of strong horseshoe maps, defined as onto maps whose phase spaces act as attractors for their inverse iterations. We prove that such maps, when possessing the reverse bounded distortion property, are doubly ergodic with respect to the Lebesgue measure. Additionally, we establish the robustness of double ergodicity and weak mixing for a <span>(C^1)</span>-perturbed doubling map on the circle, demonstrating that all maps in a <span>(C^1)</span>-neighborhood, as given in Theorem B, share these properties.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"425 - 431"},"PeriodicalIF":0.5,"publicationDate":"2026-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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-solutions to mixed equations in acylindrically hyperbolic groups coming from random walks 随机漫步的非圆柱形双曲群混合方程的非解
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-03 DOI: 10.1007/s00013-026-02223-4
Henry Bradford, Alessandro Sisto
{"title":"Non-solutions to mixed equations in acylindrically hyperbolic groups coming from random walks","authors":"Henry Bradford,&nbsp;Alessandro Sisto","doi":"10.1007/s00013-026-02223-4","DOIUrl":"10.1007/s00013-026-02223-4","url":null,"abstract":"<div><p>A mixed equation in a group <i>G</i> is given by a non-trivial element <i>w</i>(<i>x</i>) of the free product <span>(G *mathbb {Z})</span>, and a solution is some <span>(gin G)</span> such that <i>w</i>(<i>g</i>) is the identity. For <i>G</i> acylindrically hyperbolic with trivial finite radical (e.g. torsion-free), we show that any mixed equation of length <i>n</i> has a non-solution of length comparable to <span>(log (n))</span>, which is the best possible bound. Similarly, we show that there is a common non-solution of length <i>O</i>(<i>n</i>) to all mixed equations of length <i>n</i>, again the best possible bound. In fact, in both cases, we show that a random walk of appropriate length yields a non-solution with positive probability.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"343 - 350"},"PeriodicalIF":0.5,"publicationDate":"2026-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-026-02223-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 adjoint orbits in nilpotent ideals of a Borel subalgebra Borel子代数的幂零理想中的伴随轨道
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-02-09 DOI: 10.1007/s00013-025-02218-7
Rupert W. T. Yu
{"title":"On adjoint orbits in nilpotent ideals of a Borel subalgebra","authors":"Rupert W. T. Yu","doi":"10.1007/s00013-025-02218-7","DOIUrl":"10.1007/s00013-025-02218-7","url":null,"abstract":"<div><p>Let <span>(mathfrak {m})</span> be a nilpotent ideal in the Borel subalgebra <span>(mathfrak {b})</span> of a complex finite-dimensional semisimple Lie algebra, and <span>(mathfrak {m}^{bullet })</span> the subset of (ad-)nilpotent elements in <span>(mathfrak {b})</span> such that <span>(mathfrak {m})</span> is the minimal ideal containing them. This set is stable under the adjoint action of the corresponding Borel subgroup <span>(textbf{B})</span>. We prove that <span>(mathfrak {m}^{bullet })</span> contains a unique closed <span>(textbf{B})</span>-orbit which is the orbit of a nilpotent element whose support is the set of minimal roots associated to the root space decomposition of <span>(mathfrak {m})</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"365 - 375"},"PeriodicalIF":0.5,"publicationDate":"2026-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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