Mathematische Nachrichten最新文献

{"title":"Equivariant birational types and derived categories","authors":"Christian Böhning,&nbsp;Hans-Christian Graf von Bothmer,&nbsp;Yuri Tschinkel","doi":"10.1002/mana.202400006","DOIUrl":"https://doi.org/10.1002/mana.202400006","url":null,"abstract":"<p>We investigate equivariant birational geometry of rational surfaces and threefolds from the perspective of derived categories.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 11","pages":"4333-4355"},"PeriodicalIF":0.8,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142642524","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 locally finite groups whose derived subgroup is locally nilpotent","authors":"Marco Trombetti","doi":"10.1002/mana.202400263","DOIUrl":"https://doi.org/10.1002/mana.202400263","url":null,"abstract":"<p>A celebrated theorem of Helmut Wielandt shows that the nilpotent residual of the subgroup generated by two subnormal subgroups of a finite group is the subgroup generated by the nilpotent residuals of the subgroups. This result has been extended to saturated formations in Ballester-Bolinches, Ezquerro, and Pedreza-Aguilera [Math. Nachr. 239–240 (2002), 5–10]. Although Wielandt's result is not true in arbitrary locally finite groups, we are able to extend it (even in a stronger form) to homomorphic images of periodic linear groups. Also, all results in Ballester-Bolinches, Ezquerro, and Pedreza-Aguilera [Math. Nachr. 239–240 (2002), 5–10] are extended to locally finite groups, so it is possible to characterize the class of locally finite groups with a locally nilpotent derived subgroup as the largest subgroup-closed saturated formation <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$mathfrak {X}$</annotation>\u0000 </semantics></math> such that, for all <span></span><math>\u0000 <semantics>\u0000 <mi>SL</mi>\u0000 <annotation>$mathbf {SL}$</annotation>\u0000 </semantics></math>-closed saturated formations <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathfrak {F}$</annotation>\u0000 </semantics></math>, the <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathfrak {F}$</annotation>\u0000 </semantics></math>-residual of an <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$mathfrak {X}$</annotation>\u0000 </semantics></math>-group generated by <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathfrak {F}$</annotation>\u0000 </semantics></math>-subnormal subgroups is the subgroup generated by their <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathfrak {F}$</annotation>\u0000 </semantics></math>-residuals. Our proofs are based on a reduction theorem that is of an independent interest. Furthermore, we provide strengthened versions of Wielandt's result for other relevant classes of groups, among which we mention the class of paranilpotent groups. A brief discussion on the permutability of the residuals is given at the end of the paper.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4389-4400"},"PeriodicalIF":0.8,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400263","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862252","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":"Well-posedness of the two-dimensional stationary Navier–Stokes equations around a uniform flow","authors":"Mikihiro Fujii,&nbsp;Hiroyuki Tsurumi","doi":"10.1002/mana.202400011","DOIUrl":"https://doi.org/10.1002/mana.202400011","url":null,"abstract":"<p>In this paper, we consider the solvability of the two-dimensional stationary Navier–Stokes equations on the whole plane <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>. In Fujii [Ann. PDE, 10 (2024), no. 1. Paper No. 10], it was proved that the stationary Navier–Stokes equations on <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> is ill-posed for solutions around zero. In contrast, considering solutions around the nonzero constant flow, the perturbed system has a better regularity in the linear part, which enables us to prove the unique existence of solutions in the scaling critical spaces of the Besov type.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4401-4415"},"PeriodicalIF":0.8,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862093","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":"There is no 290-Theorem for higher degree forms","authors":"Vítězslav Kala,&nbsp;Om Prakash","doi":"10.1002/mana.202400253","DOIUrl":"https://doi.org/10.1002/mana.202400253","url":null,"abstract":"<p>We study the universality of forms of degrees greater than 2 over rings of integers of totally real number fields. We show that such universal forms always exist, but cannot be characterized by any variant of the 290-Theorem of Bhargava–Hanke.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 11","pages":"4322-4332"},"PeriodicalIF":0.8,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400253","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142642536","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":"Note on intrinsic metrics on graphs","authors":"Daniel Lenz,&nbsp;Marcel Schmidt,&nbsp;Felix Seifert","doi":"10.1002/mana.202400099","DOIUrl":"https://doi.org/10.1002/mana.202400099","url":null,"abstract":"<p>We study the set of intrinsic metrics on a given graph. This is a convex compact set and it carries a natural order. We investigate existence of largest elements with respect to this order. We show that the only locally finite graphs which admit a largest intrinsic metric are certain finite star graphs. In particular, all infinite locally finite graphs do not admit a largest intrinsic metric. For infinite graphs which are not locally finite the set of intrinsic metrics may be trivial as we show by an example. Moreover, we give a characterization for the existence of intrinsic metrics with finite balls for weakly spherically symmetric graphs.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 11","pages":"4307-4321"},"PeriodicalIF":0.8,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142642324","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":"Nonconcentration phenomenon for one-dimensional reaction–diffusion systems with mass dissipation","authors":"Juan Yang,&nbsp;Anna Kostianko,&nbsp;Chunyou Sun,&nbsp;Bao Quoc Tang,&nbsp;Sergey Zelik","doi":"10.1002/mana.202300442","DOIUrl":"https://doi.org/10.1002/mana.202300442","url":null,"abstract":"<p>Reaction–diffusion systems with mass dissipation are known to possess blow-up solutions in high dimensions when the nonlinearities have super quadratic growth rates. In dimension 1, it has been shown recently that one can have global existence of bounded solutions if nonlinearities are at most cubic. For the cubic intermediate sum condition, that is, nonlinearities might have arbitrarily high growth rates, an additional entropy inequality had to be imposed. In this paper, we remove this extra entropy assumption completely and obtain global boundedness for reaction–diffusion systems with cubic intermediate sum condition. The novel idea is to show a nonconcentration phenomenon for mass dissipating systems, that is the mass dissipation implies a dissipation in a Morrey space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>M</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>δ</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathsf {M}^{1,delta }(Omega)$</annotation>\u0000 </semantics></math> for some <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$delta &amp;gt;0$</annotation>\u0000 </semantics></math>. As far as we are concerned, it is the first time such a bound is derived for mass dissipating reaction–diffusion systems. The results are then applied to obtain global existence and boundedness of solutions to an oscillatory Belousov–Zhabotinsky system, which satisfies cubic intermediate sum condition but does not fulfill the entropy assumption. Extensions include global existence mass controlled systems with slightly super cubic intermediate sum condition.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 11","pages":"4288-4306"},"PeriodicalIF":0.8,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300442","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142642113","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":"Twisted Kähler–Einstein metrics on flag varieties","authors":"Eder M. Correa,&nbsp;Lino Grama","doi":"10.1002/mana.202300553","DOIUrl":"10.1002/mana.202300553","url":null,"abstract":"<p>In this paper, we present a description of invariant twisted Kähler–Einstein (tKE) metrics on flag varieties. Additionally, we delve into the applications of the concepts utilized in proving our main result, particularly concerning the existence of the invariant twisted constant scalar curvature Kähler metrics. Moreover, we provide a precise description of the greatest Ricci lower bound for arbitrary Kähler classes on flag varieties. From this description, we establish a sequence of inequalities linked to optimal upper bounds for the volume of Kähler metrics, relying solely on tools derived from the Lie theory. Further, we illustrate our main results through various examples, encompassing full flag varieties, the projectivization of the tangent bundle of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>${mathbb {P}}^{n+1}$</annotation>\u0000 </semantics></math>, and families of flag varieties with a Picard number 2.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 11","pages":"4273-4287"},"PeriodicalIF":0.8,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252029","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":"Inverse initial-value problems for time fractional diffusion equations in fractional Sobolev spaces","authors":"Nguyen Huy Tuan,&nbsp;Bao-Ngoc Tran","doi":"10.1002/mana.202300292","DOIUrl":"10.1002/mana.202300292","url":null,"abstract":"&lt;p&gt;We study the time fractional diffusion equation &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;∂&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;G&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;/mrow&gt;\u0000 &lt;annotation&gt;$partial _t u = partial _t^{1-alpha } mathcal {A} u + G(u)$&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;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$0&amp;lt;alpha &amp;lt;1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, in a bounded domain &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;⊂&lt;/mo&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;/mrow&gt;\u0000 &lt;annotation&gt;$Omega subset mathbb {R}^N$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with an elliptic operator &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {A}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and a locally Lipschitz nonlinearity &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; on fractional Sobolev spaces, subjected to the homogeneous Dirichlet boundary condition. Data have not been measured at the initial time &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&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;$t=0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, but at a final time &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;T&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;$T&amp;gt;0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, that is, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$u(","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 11","pages":"4182-4213"},"PeriodicalIF":0.8,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176967","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 a family of sparse exponential sums","authors":"Moubariz Z. Garaev,&nbsp;Zeev Rudnick,&nbsp;Igor E. Shparlinski","doi":"10.1002/mana.202300426","DOIUrl":"10.1002/mana.202300426","url":null,"abstract":"<p>We investigate exponential sums modulo primes whose phase function is a sparse polynomial, with exponents growing with the prime. In particular, such sums model those which appear in the study of the quantum cat map. While they are not amenable to treatment by algebro-geometric methods such as Weil's bounds, Bourgain gave a nontrivial estimate for these and more general sums. In this work, we obtain explicit bounds with reasonable savings over various types of averaging. We also initiate the study of the value distribution of these sums.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 11","pages":"4214-4231"},"PeriodicalIF":0.8,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300426","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176968","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 a parabolic Monge–Ampère type equation on compact almost Hermitian manifolds","authors":"Masaya Kawamura","doi":"10.1002/mana.202300155","DOIUrl":"10.1002/mana.202300155","url":null,"abstract":"<p>We investigate a parabolic Monge–Ampère type equation on compact almost Hermitian manifolds and derive a priori gradient and second-order derivative estimates for solutions to this parabolic equation. These a priori estimates give us higher order estimates and a long-time solution. Then, we can observe its behavior as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>→</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$trightarrow infty$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 11","pages":"4232-4272"},"PeriodicalIF":0.8,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176985","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}