Mathematische Nachrichten最新文献

{"title":"The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds","authors":"Isolda Cardoso,&nbsp;Ana Cosgaya,&nbsp;Silvio Reggiani","doi":"10.1002/mana.202400213","DOIUrl":"https://doi.org/10.1002/mana.202400213","url":null,"abstract":"<p>A real Lie algebra is said to be characteristically solvable if its derivation algebra is solvable. We explicitly determine the moduli space of left-invariant metrics, up to isometric automorphism, for 6-dimensional nilmanifolds whose associated Lie algebra is characteristically solvable of triangular type. We also compute the corresponding full isometry groups. For each left-invariant metric on these nilmanifolds we compute the index and distribution of symmetry. In particular, we find the first known examples of Lie groups which do not admit a left-invariant metric with positive index of symmetry. As an application we study the index of symmetry of nilsoliton metrics. We prove that nilsoliton metrics detect the existence of left-invariant metrics with positive index of symmetry.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 5","pages":"1496-1520"},"PeriodicalIF":0.8,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930502","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":"Characterizations of the Sobolev space H1 on the boundary of a strongly Lipschitz domain in 3-D","authors":"Nathanael Skrepek","doi":"10.1002/mana.202400282","DOIUrl":"https://doi.org/10.1002/mana.202400282","url":null,"abstract":"<p>In this work, we investigate the Sobolev space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>∂</mi>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathrm{H}^{1}(partial Omega)$</annotation>\u0000 </semantics></math> on a strongly Lipschitz boundary <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>∂</mi>\u0000 <mi>Ω</mi>\u0000 </mrow>\u0000 <annotation>$partial Omega$</annotation>\u0000 </semantics></math>, that is, <span></span><math>\u0000 <semantics>\u0000 <mi>Ω</mi>\u0000 <annotation>$Omega$</annotation>\u0000 </semantics></math> is a strongly Lipschitz domain (not necessarily bounded). In most of the literature, this space is defined via charts and Sobolev spaces on flat domains. We show that there is a different approach via differential operators on <span></span><math>\u0000 <semantics>\u0000 <mi>Ω</mi>\u0000 <annotation>$Omega$</annotation>\u0000 </semantics></math> and a weak formulation directly on the boundary that leads to the same space. This second characterization of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>∂</mi>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathrm{H}^{1}(partial Omega)$</annotation>\u0000 </semantics></math> is in particular of advantage, when it comes to traces of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 <mo>(</mo>\u0000 <mo>curl</mo>\u0000 <mo>,</mo>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{H}(operatorname{curl},Omega)$</annotation>\u0000 </semantics></math> vector fields.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1342-1355"},"PeriodicalIF":0.8,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400282","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809571","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":"Nonstandard representation of the Dirichlet form and application to the comparison theorem","authors":"Haosui Duanmu,&nbsp;Aaron Smith","doi":"10.1002/mana.202300246","DOIUrl":"https://doi.org/10.1002/mana.202300246","url":null,"abstract":"<p>The Dirichlet form is a generalization of the Laplacian, heavily used in the study of many diffusion-like processes. In this paper, we present a <i>nonstandard representation theorem</i> for the Dirichlet form, showing that the usual Dirichlet form can be well-approximated by a <i>hyperfinite</i> sum. One of the main motivations for such a result is to provide a tool for directly translating results about Dirichlet forms on finite or countable state spaces to results on more general state spaces, without having to translate the details of the proofs. As an application, we compare the Dirichlet forms of two general Markov processes by applying the transfer of the well-known comparison theorem for finite Markov processes.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1167-1183"},"PeriodicalIF":0.8,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300246","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809762","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":"M\u0000 $M$\u0000 -Ideals in real operator algebras","authors":"David P. Blecher,&nbsp;Matthew Neal,&nbsp;Antonio M. Peralta,&nbsp;Shanshan Su","doi":"10.1002/mana.202400227","DOIUrl":"https://doi.org/10.1002/mana.202400227","url":null,"abstract":"<p>In a recent paper, we showed that a subspace of a real <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>JBW</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${rm JBW}^*$</annotation>\u0000 </semantics></math>-triple is an <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>-summand if and only if it is a <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>weak</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${rm weak}^*$</annotation>\u0000 </semantics></math>-closed triple ideal. As a consequence, <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>-ideals of real <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>JB</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${rm JB}^*$</annotation>\u0000 </semantics></math>-triples, including real <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${rm C}^*$</annotation>\u0000 </semantics></math>-algebras, real <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>JB</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${rm JB}^*$</annotation>\u0000 </semantics></math>-algebras and real TROs, correspond to norm-closed triple ideals. In this paper, we extend this result by identifying the <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>-ideals in (possibly non-self-adjoint) real operator algebras and Jordan operator algebras. The argument for this is necessarily different. We also give simple characterizations of one-sided <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>-ideals in real operator algebras, and give some applications to that theory.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1328-1341"},"PeriodicalIF":0.8,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809763","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 characterization of some finite simple groups by their character codegrees","authors":"Hung P. Tong-Viet","doi":"10.1002/mana.202400283","DOIUrl":"https://doi.org/10.1002/mana.202400283","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a finite group and let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;annotation&gt;$chi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a complex irreducible character of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. The codegree of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;annotation&gt;$chi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is defined by &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;cod&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&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;mi&gt;ker&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;χ&lt;/mi&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;annotation&gt;$textrm {cod}(chi)=|G:textrm {ker}(chi)|/chi (1)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ker&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$textrm {ker}(chi)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the kernel of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;annotation&gt;$chi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. In this paper, we show that if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;annotation&gt;$H$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a finite simple exceptional group of Lie type or a finite simple projective special linear group and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is any finite group such that the character codegree sets of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&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;H&lt;/mi&gt;\u0000 &lt;annotation&gt;$H$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; coincide, then &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;ann","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1356-1369"},"PeriodicalIF":0.8,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400283","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809664","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":"Hodge loci associated with linear subspaces intersecting in codimension one","authors":"Remke Kloosterman","doi":"10.1002/mana.202400066","DOIUrl":"https://doi.org/10.1002/mana.202400066","url":null,"abstract":"&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;X&lt;/mi&gt;\u0000 &lt;mo&gt;⊂&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;k&lt;/mi&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;annotation&gt;$Xsubset mathbf {P}^{2k+1}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a smooth hypersurface containing two &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;annotation&gt;$k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-dimensional linear spaces &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Π&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Π&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Pi _1,Pi _2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, such that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;dim&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Π&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;∩&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Π&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;k&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;$dim Pi _1cap Pi _2=k-1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. In this paper, we study the question whether the Hodge loci &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;NL&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Π&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Π&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&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;$operatorname{NL}([Pi _1]+lambda [Pi _2])$&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 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1220-1229"},"PeriodicalIF":0.8,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400066","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809959","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":"Variable Hardy spaces on spaces of homogeneous type and applications to variable Hardy spaces associated with elliptic operators having Robin boundary conditions on Lipschitz domains","authors":"Xiong Liu,&nbsp;Wenhua Wang","doi":"10.1002/mana.202400300","DOIUrl":"https://doi.org/10.1002/mana.202400300","url":null,"abstract":"&lt;p&gt;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;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(mathcal {X},d,mu)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a space of homogeneous type with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;μ&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;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mu (mathcal {X})&lt;infty$&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;p&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;·&lt;/mo&gt;\u0000 &lt;mo&gt;)&lt;/mo&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;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$p(cdot):mathcal {X}rightarrow (0,infty)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; a variable exponent function satisfying &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;msub&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$0&lt;p_-&lt;infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;ess&lt;/mi&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;inf&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mi&gt;p&lt;/mi&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;/mrow&gt;\u0000 &lt;annotation&gt;$p_-:=mathrm{ess inf}_{xin mathcal {X}}p(x)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Assume that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$L$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a nonnegative self-adjoint operator on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1370-1440"},"PeriodicalIF":0.8,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809954","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":"Studies on a system of nonlinear Schrödinger equations with potential and quadratic interaction","authors":"Vicente Alvarez,&nbsp;Amin Esfahani","doi":"10.1002/mana.202400068","DOIUrl":"https://doi.org/10.1002/mana.202400068","url":null,"abstract":"<p>In this work, we study the existence of various classes of standing waves for a nonlinear Schrödinger system with quadratic interaction, along with a harmonic or partially harmonic potential. We establish the existence of ground-state normalized solutions for this system, which serve as local minimizers of the associated functionals. To address the difficulties raised by the potential term, we employ profile decomposition and concentration-compactness principles. The absence of global energy minimizers in critical and supercritical cases leads us to focus on local energy minimizers. Positive results arise in scenarios of partial confinement, attributed to the spectral properties of the associated linear operators. Furthermore, we demonstrate the existence of a second normalized solution using the Mountain-pass geometry, effectively navigating the difficulties posed by the nonlinear terms. We also explore the asymptotic behavior of local minimizers, revealing connections with unique eigenvectors of the linear operators. Additionally, we identify global and blow-up solutions over time under specific conditions, contributing new insights into the dynamics of the system.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1230-1303"},"PeriodicalIF":0.8,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809544","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":"Two-pointed Prym–Brill–Noether loci and coupled Prym–Petri theorem","authors":"Minyoung Jeon","doi":"10.1002/mana.202300581","DOIUrl":"https://doi.org/10.1002/mana.202300581","url":null,"abstract":"<p>We establish two-pointed Prym–Brill–Noether loci with special vanishing at two points, and determine their K-theory classes when the dimensions are as expected. The classes are derived by the applications of a formula for the K-theory of certain vexillary degeneracy loci in type D. In particular, we show a two-pointed version of the Prym–Petri theorem on the expected dimension in the general case, with a coupled Prym–Petri map. Our approach is inspired by the work on pointed cases by Tarasca, and we generalize unpointed cases by De Concini-Pragacz and Welters.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1201-1219"},"PeriodicalIF":0.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809702","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":"Subelliptic \u0000 \u0000 p\u0000 $p$\u0000 -Laplacian spectral problem for Hörmander vector fields","authors":"Mukhtar Karazym,&nbsp;Durvudkhan Suragan","doi":"10.1002/mana.202300513","DOIUrl":"https://doi.org/10.1002/mana.202300513","url":null,"abstract":"<p>Based on variational methods, we study the spectral problem for the subelliptic <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-Laplacian arising from smooth Hörmander vector fields. We derive the smallest eigenvalue, prove its simplicity and isolatedness, establish the positivity of the first eigenfunction, and show Hölder regularity of eigenfunctions with respect to the control distance. Moreover, we determine the best constant for the <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <annotation>$L^{p}$</annotation>\u0000 </semantics></math>-Poincaré–Friedrichs inequality for Hörmander vector fields as a byproduct.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1184-1200"},"PeriodicalIF":0.8,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809868","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}