Mathematische Nachrichten最新文献

{"title":"Busemann functions and uniformization of Gromov hyperbolic spaces","authors":"Qingshan Zhou,&nbsp;Saminathan Ponnusamy,&nbsp;Antti Rasila","doi":"10.1002/mana.12017","DOIUrl":"https://doi.org/10.1002/mana.12017","url":null,"abstract":"<p>The uniformization theory of Gromov hyperbolic spaces investigated by Bonk, Heinonen, and Koskela, generalizes the case where a classical Poincaré ball type model is used as the starting point. In this paper, we develop this approach in the case where the underlying domain is unbounded, corresponding to the classical Poincaré half-space model. More precisely, we study conformal densities via Busemann functions on Gromov hyperbolic spaces and prove that the deformed spaces are unbounded uniform spaces. Furthermore, we show that there is a one-to-one correspondence between the bilipschitz classes of proper geodesic Gromov hyperbolic spaces that are roughly starlike with respect to a point on the Gromov boundary and the quasisimilarity classes of unbounded locally compact uniform spaces. Our result can be understood as an unbounded counterpart of the main result of Bonk, Heinonen, and Koskela, <i>Uniformizing Gromov hyperbolic spaces</i>, Astérisque. <b>270</b> (2001).</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 7","pages":"2152-2176"},"PeriodicalIF":0.8,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144657656","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":"Global and microlocal aspects of Dirac operators: Propagators and Hadamard states","authors":"Matteo Capoferri,&nbsp;Simone Murro","doi":"10.1002/mana.12032","DOIUrl":"https://doi.org/10.1002/mana.12032","url":null,"abstract":"<p>We propose a geometric approach to construct the Cauchy evolution operator for the Lorentzian Dirac operator on Cauchy-compact globally hyperbolic 4-manifolds. We realize the Cauchy evolution operator as the sum of two invariantly defined oscillatory integrals—the <i>positive</i> and <i>negative</i> Dirac propagators—global in space and in time, with distinguished complex-valued geometric phase functions. As applications, we relate the Cauchy evolution operators with the Feynman propagator and construct Cauchy surfaces covariances of quasifree Hadamard states.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 9","pages":"2942-2974"},"PeriodicalIF":0.8,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.12032","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145038549","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 the Lane–Emden–Matukuma equation \u0000 \u0000 \u0000 −\u0000 Δ\u0000 u\u0000 =\u0000 \u0000 \u0000 (\u0000 1\u0000 +\u0000 |\u0000 x\u0000 |\u0000 \u0000 2\u0000 \u0000 \u0000 )\u0000 \u0000 \u0000 \u0000 \u0000 −\u0000 σ\u0000 \u0000 \u0000 \u0000 u\u0000 α\u0000 \u0000 \u0000 $-Delta u = (1+|x|^2){}^{-sigma } u^alpha$\u0000 in \u0000 \u0000 \u0000 R\u0000 n\u0000 \u0000 $mathbf {R}^n$\u0000 with \u0000 \u0000 \u0000 σ\u0000 >\u0000 1\u0000 \u0000 $sigma >1$","authors":"Cao Thanh Tinh","doi":"10.1002/mana.70001","DOIUrl":"https://doi.org/10.1002/mana.70001","url":null,"abstract":"<p>Of interest in this work is the following equation:\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2459-2475"},"PeriodicalIF":0.8,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144833329","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 \u0000 \u0000 \u0000 (\u0000 μ\u0000 ,\u0000 ν\u0000 )\u0000 \u0000 $(mu,nu)$\u0000 -dichotomies via admissibility","authors":"Lucas Backes,&nbsp;Davor Dragičević","doi":"10.1002/mana.70005","DOIUrl":"https://doi.org/10.1002/mana.70005","url":null,"abstract":"<p>We present a characterization of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>μ</mi>\u0000 <mo>,</mo>\u0000 <mi>ν</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(mu,nu)$</annotation>\u0000 </semantics></math>-dichotomies in terms of the admissibility of certain pairs of weighted spaces for nonautonomous discrete time dynamics acting on Banach spaces. Our general framework enables us to treat various settings in which no similar result has been previously obtained as well as to recover and refine several known results. We emphasize that our results hold without any bounded growth assumption and the statements make no use of Lyapunov norms. Moreover, as a consequence of our characterization, we study the robustness of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>μ</mi>\u0000 <mo>,</mo>\u0000 <mi>ν</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(mu, nu)$</annotation>\u0000 </semantics></math>-dichotomies, that is, we show that this notion persists under small but very general linear perturbations.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2547-2569"},"PeriodicalIF":0.8,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144833327","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":"Qualitative properties for the 2-\u0000 \u0000 D\u0000 $D$\u0000 nonautonomous stochastic Navier–Stokes equations","authors":"Dingshi Li,&nbsp;Shaoyue Mi","doi":"10.1002/mana.12015","DOIUrl":"https://doi.org/10.1002/mana.12015","url":null,"abstract":"<p>We establish the pullback asymptotic compact of the family probability measures with respect to probability distributions of the solutions of the 2-<span></span><math>\u0000 <semantics>\u0000 <mi>D</mi>\u0000 <annotation>$D$</annotation>\u0000 </semantics></math> nonautonomous stochastic Navier–Stokes equations, and prove the existence and uniqueness of a pullback measure attractor. The structures of pullback measure attractors is characterized by complete solutions, which is an extension of the notation of evolution systems of measures introduced and developed by Da Prato and Röckner in [Rendiconti Lincei-Matematica e Applicazioni <b>17</b> (2006), no. 4, 397–403] and [Seminar on Stochastic Analysis, Random Fields and Applications, 115–122, Springer, 2007]. Moreover, for stochastic systems containing periodic deterministic forcing terms, we show the pullback measure attractors are also periodic under certain conditions.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 7","pages":"2085-2104"},"PeriodicalIF":0.8,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144657637","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":"Positive solution for the Kirchhoff-type equation with supercritical concave and convex nonlinearities","authors":"Liying Shan,&nbsp;Wei Shuai","doi":"10.1002/mana.70002","DOIUrl":"https://doi.org/10.1002/mana.70002","url":null,"abstract":"<p>We study the following Kirchhoff-type equation\u0000\u0000 </p><p>Via a new variational principle established by Moameni (C. R. Math. Acad. Sci. Paris. <b>355</b> (2017) 1236–1241), we shall show that, for each <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$p&gt;2$</annotation>\u0000 </semantics></math>, there exists <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>λ</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$lambda ^*&gt;0$</annotation>\u0000 </semantics></math> such that for each <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <msup>\u0000 <mi>λ</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$lambda in (0,lambda ^*)$</annotation>\u0000 </semantics></math> Equation (0.1) has a positive solution with negative energy. Furthermore, by using the improved Clark theorem, we can obtain a sequence of solutions with negative energy converging to zero in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$L^{infty }(Omega)$</annotation>\u0000 </semantics></math> without the restriction of <span></span><math>\u0000 <semantics>\u0000 <mi>λ</mi>\u0000 <annotation>$lambda$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2476-2492"},"PeriodicalIF":0.8,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144833045","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":"Carleson measures on domains in Heisenberg groups","authors":"Tomasz Adamowicz,&nbsp;Marcin Gryszówka","doi":"10.1002/mana.12038","DOIUrl":"https://doi.org/10.1002/mana.12038","url":null,"abstract":"<p>We study the Carleson measures on nontangentially accessible (NTA) and admissible for the Dirichlet problem (ADP) domains in the Heisenberg groups <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {H}^n$</annotation>\u0000 </semantics></math> and provide two characterizations of such measures: (1) in terms of the level sets of subelliptic harmonic functions and (2) via the 1-quasiconformal family of mappings on the Korányi–Reimann unit ball. Moreover, we establish the <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$L^2$</annotation>\u0000 </semantics></math>-bounds for the square function <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>S</mi>\u0000 <mi>α</mi>\u0000 </msub>\u0000 <annotation>$S_{alpha }$</annotation>\u0000 </semantics></math> of a subelliptic harmonic function and the Carleson measure estimates for the BMO boundary data, both on NTA domains in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {H}^n$</annotation>\u0000 </semantics></math>. Finally, we prove a Fatou-type theorem on <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>ε</mi>\u0000 <mo>,</mo>\u0000 <mi>δ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(varepsilon, delta)$</annotation>\u0000 </semantics></math>-domains in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {H}^n$</annotation>\u0000 </semantics></math>. Our work generalizes results by Capogna–Garofalo and Jerison–Kenig.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 7","pages":"2424-2452"},"PeriodicalIF":0.8,"publicationDate":"2025-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144657636","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":"Optimality of embeddings in Orlicz spaces","authors":"Tomáš Beránek","doi":"10.1002/mana.12036","DOIUrl":"https://doi.org/10.1002/mana.12036","url":null,"abstract":"<p>Working with function spaces in various branches of mathematical analysis introduces optimality problems, where the question of choosing a function space both accessible and expressive becomes a nontrivial exercise. A good middle ground is provided by Orlicz spaces, parameterized by a single Young function and thus accessible, yet expansive. In this work, we study optimality problems on Sobolev embeddings in the so-called Maz'ya classes of Euclidean domains which are defined through their isoperimetric behavior. In particular, we prove the non-existence of optimal Orlicz spaces in certain Orlicz–Sobolev embeddings in a limiting (critical) state, whose pivotal special case is the celebrated embedding of Brezis and Wainger for John domains.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 7","pages":"2380-2400"},"PeriodicalIF":0.8,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.12036","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144657568","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 some properties of the asymptotic Samuel function","authors":"A. Bravo,&nbsp;S. Encinas,&nbsp;J. Guillán-Rial","doi":"10.1002/mana.12037","DOIUrl":"https://doi.org/10.1002/mana.12037","url":null,"abstract":"<p>The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. Here, we explore some natural properties in the context of excellent, equidimensional rings containing a field. In addition, we establish some results regarding the Samuel slope of a local ring. This is an invariant related with algorithmic resolution of singularities of algebraic varieties. Among other results, we study its behavior after certain faithfully flat extensions.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 7","pages":"2401-2423"},"PeriodicalIF":0.8,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.12037","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144657569","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":"Topology of a complex double-plane branching along a real line arrangement","authors":"Ichiro Shimada","doi":"10.1002/mana.12023","DOIUrl":"https://doi.org/10.1002/mana.12023","url":null,"abstract":"<p>We investigate the topology of the double cover of the complex affine plane branching along a nodal real line arrangement. We define certain topological 2-cycles in the double plane using the real structure of the arrangement, and calculate their intersection numbers.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 7","pages":"2204-2241"},"PeriodicalIF":0.8,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144657567","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}