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":"Existence of a local strong solution to the beam–polymeric fluid interaction system","authors":"Dominic Breit,&nbsp;Prince Romeo Mensah","doi":"10.1002/mana.12030","DOIUrl":"https://doi.org/10.1002/mana.12030","url":null,"abstract":"<p>We construct a unique local strong solution to the finitely extensible nonlinear elastic (FENE) dumbbell model of Warner-type for an incompressible polymer fluid (described by the Navier–Stokes–Fokker–Planck equations) interacting with a flexible elastic shell. The latter occupies the flexible boundary of the polymer fluid domain and is modeled by a beam equation coupled through kinematic boundary conditions and the balance of forces. In the 2D case for the co-rotational Fokker–Planck model we obtain global-in-time strong solutions.</p><p>A main step in our approach is the proof of local well-posedness for just the solvent–structure system in higher-order topologies which is of independent interest. Different from most of the previous results in the literature, the reference spatial domain is an arbitrary smooth subset of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>$mathbb {R}^3$</annotation>\u0000 </semantics></math>, rather than a flat one. That is, we cover viscoelastic shells rather than elastic plates. Our results also supplement the existing literature on the Navier–Stokes–Fokker–Planck equations posed on a fixed bounded domain.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 7","pages":"2327-2379"},"PeriodicalIF":0.8,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.12030","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144657638","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":"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":"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}

{"title":"Correlations of fractions whose denominators are products of primes","authors":"Meijie Lu","doi":"10.1002/mana.12027","DOIUrl":"https://doi.org/10.1002/mana.12027","url":null,"abstract":"<p>In this paper, we focus on the pair correlation of fractions whose denominators are products of primes. We show that the limiting pair correlation function of such fractions on any short interval <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>I</mi>\u0000 <mo>⊂</mo>\u0000 <mo>[</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>${bf I}subset [0,1]$</annotation>\u0000 </semantics></math> exists and is independent of <span></span><math>\u0000 <semantics>\u0000 <mi>I</mi>\u0000 <annotation>${bf I}$</annotation>\u0000 </semantics></math>. Furthermore, we use this result to compute the pair correlation function of the angles of elements in specific types of regions.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 7","pages":"2263-2281"},"PeriodicalIF":0.8,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144657595","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":"General infinitesimal variations of the Hodge structure of ample curves in surfaces","authors":"Víctor González-Alonso,&nbsp;Sara Torelli","doi":"10.1002/mana.12028","DOIUrl":"https://doi.org/10.1002/mana.12028","url":null,"abstract":"<p>Given a smooth projective complex curve inside a smooth projective surface, one can ask how its Hodge structure varies when the curve moves inside the surface. In this paper, we develop a general theory to study the infinitesimal version of this question in the case of ample curves. We can then apply the machinery to show that the infinitesimal variation of the Hodge structure of a general deformation of an ample curve in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbb {P}^1times mathbb {P}^1$</annotation>\u0000 </semantics></math> is an isomorphism.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 7","pages":"2282-2308"},"PeriodicalIF":0.8,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.12028","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144657596","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":"Substochastic operators in symmetric spaces","authors":"Maciej Ciesielski,&nbsp;Grzegorz Lewicki","doi":"10.1002/mana.12029","DOIUrl":"https://doi.org/10.1002/mana.12029","url":null,"abstract":"<p>First, we solve a crucial problem under which conditions increasing uniform <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-monotonicity is equivalent to lower local uniform <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-monotonicity. Next, we investigate properties of substochastic operators on <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mo>+</mo>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$L^1+L^infty$</annotation>\u0000 </semantics></math> with applications. Namely, we show that a countable infinite combination of substochastic operators is also substochastic. Using <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-monotonicity properties, we prove several theorems devoted to the convergence of the sequence of substochastic operators in the norm of a symmetric space <span></span><math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$E$</annotation>\u0000 </semantics></math> under addition assumption on <span></span><math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$E$</annotation>\u0000 </semantics></math>. In our final discussion, we focus on compactness of admissible operators for Banach couples under additional assumption.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 7","pages":"2309-2326"},"PeriodicalIF":0.8,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144657597","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}