Mathematische Nachrichten最新文献

{"title":"On the differential geometry of smooth ruled surfaces in 4-space","authors":"Jorge Luiz Deolindo-Silva","doi":"10.1002/mana.202400295","DOIUrl":"https://doi.org/10.1002/mana.202400295","url":null,"abstract":"<p>A smooth ruled surface in 4-space has only parabolic points or inflection points of the real type. We show, by means of contact with transverse planes, that at a parabolic point, there exist two tangent directions determining two planes along which the parallel projection exhibits <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$mathcal {A}$</annotation>\u0000 </semantics></math>-singularities of type butterfly or worse. In particular, such parabolic points can be classified as butterfly hyperbolic, parabolic, or elliptic points depending on the value of the discriminant of a binary differential equation (BDE). Also, whenever such discriminant is positive, we ensure that the integral curves of these directions form a pair of foliations on the ruled surface. Moreover, the set of points that nullify the discriminant is a regular curve transverse to the regular curve formed by inflection points of the real type. Finally, using a particular projective transformation, we obtain a simple parametrization of the ruled surface such that the moduli of its 5-jet identify a butterfly hyperbolic/parabolic/elliptic point, as well as we get the stable configurations of the solutions of BDE in the discriminant curve.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4689-4704"},"PeriodicalIF":0.8,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861279","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 solvability and hypoellipticity for evolution operators on tori and spheres","authors":"Alexandre Kirilov,&nbsp;André Pedroso Kowacs,&nbsp;Wagner Augusto Almeida de Moraes","doi":"10.1002/mana.202300506","DOIUrl":"https://doi.org/10.1002/mana.202300506","url":null,"abstract":"<p>In this paper, we investigate global properties of a class of evolution differential operators defined on a product of tori and spheres. We present a comprehensive characterization of global solvability and hypoellipticity, providing necessary and sufficient conditions that involve Diophantine conditions and the connectedness of sublevel sets associated with the coefficients of the operator. Furthermore, we recover well-known results from existing literature and introduce novel contributions.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4605-4650"},"PeriodicalIF":0.8,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860668","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":"The Noether–Lefschetz locus of surfaces in \u0000 \u0000 \u0000 P\u0000 3\u0000 \u0000 ${mathbb {P}}^3$\u0000 formed by determinantal surfaces","authors":"Manuel Leal,&nbsp;César Lozano Huerta,&nbsp;Montserrat Vite","doi":"10.1002/mana.202400132","DOIUrl":"https://doi.org/10.1002/mana.202400132","url":null,"abstract":"<p>We compute the dimension of certain components of the family of smooth determinantal degree <span></span><math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math> surfaces in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>${mathbb {P}}^3$</annotation>\u0000 </semantics></math>, and show that each of them is the closure of a component of the Noether–Lefschetz locus <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mi>L</mi>\u0000 <mo>(</mo>\u0000 <mi>d</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$NL(d)$</annotation>\u0000 </semantics></math>. Our computations exhibit that smooth determinantal surfaces in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>${mathbb {P}}^3$</annotation>\u0000 </semantics></math> of degree 4 form a divisor in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <msub>\u0000 <mi>O</mi>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 </msub>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>4</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$|mathcal {O}_{{mathbb {P}}^3}(4)|$</annotation>\u0000 </semantics></math> with five irreducible components. We will compute the degrees of each of these components: <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>320</mn>\u0000 <mo>,</mo>\u0000 <mn>2508</mn>\u0000 <mo>,</mo>\u0000 <mn>136512</mn>\u0000 <mo>,</mo>\u0000 <mn>38475</mn>\u0000 </mrow>\u0000 <annotation>$320,2508,136512,38475$</annotation>\u0000 </semantics></math>, and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>320112</mn>\u0000 </mrow>\u0000 <annotation>$hskip.001pt 320112$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4671-4688"},"PeriodicalIF":0.8,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860930","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":"Curvature and Weitzenböck formula for spectral triples","authors":"Bram Mesland,&nbsp;Adam Rennie","doi":"10.1002/mana.202400158","DOIUrl":"https://doi.org/10.1002/mana.202400158","url":null,"abstract":"<p>Using the Levi-Civita connection on the noncommutative differential 1-forms of a spectral triple <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>B</mi>\u0000 <mo>,</mo>\u0000 <mi>H</mi>\u0000 <mo>,</mo>\u0000 <mi>D</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(mathcal {B},mathcal {H},mathcal {D})$</annotation>\u0000 </semantics></math>, we define the full Riemann curvature tensor, the Ricci curvature tensor and scalar curvature. We give a definition of Dirac spectral triples and derive a general Weitzenböck formula for them. We apply these tools to <span></span><math>\u0000 <semantics>\u0000 <mi>θ</mi>\u0000 <annotation>$theta$</annotation>\u0000 </semantics></math>-deformations of compact Riemannian manifolds. We show that the Riemann and Ricci tensors transform naturally under <span></span><math>\u0000 <semantics>\u0000 <mi>θ</mi>\u0000 <annotation>$theta$</annotation>\u0000 </semantics></math>-deformation, whereas the connection Laplacian, Clifford representation of the curvature, and the scalar curvature are all invariant under deformation.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4582-4604"},"PeriodicalIF":0.8,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400158","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860667","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 Riemannian 4-manifolds and their twistor spaces: A moving frame approach","authors":"Giovanni Catino,&nbsp;Davide Dameno,&nbsp;Paolo Mastrolia","doi":"10.1002/mana.202300577","DOIUrl":"https://doi.org/10.1002/mana.202300577","url":null,"abstract":"<p>In this paper, we study the twistor space <span></span><math>\u0000 <semantics>\u0000 <mi>Z</mi>\u0000 <annotation>$Z$</annotation>\u0000 </semantics></math> of an oriented Riemannian 4-manifold <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> using the moving frame approach, focusing, in particular, on the Einstein, non-self-dual setting. We prove that any general first-order linear condition on the almost complex structures of <span></span><math>\u0000 <semantics>\u0000 <mi>Z</mi>\u0000 <annotation>$Z$</annotation>\u0000 </semantics></math> forces the underlying manifold <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> to be self-dual, also recovering most of the known related rigidity results. Thus, we are naturally lead to consider first-order quadratic conditions, showing that the Atiyah–Hitchin–Singer almost Hermitian twistor space of an Einstein 4-manifold bears a resemblance, in a suitable sense, to a nearly Kähler manifold.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4651-4670"},"PeriodicalIF":0.8,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300577","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860666","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":"Visco-elastic damped wave models with time-dependent coefficient","authors":"Halit Sevki Aslan,&nbsp;Michael Reissig","doi":"10.1002/mana.202300341","DOIUrl":"https://doi.org/10.1002/mana.202300341","url":null,"abstract":"<p>In this paper, we study the following Cauchy problem for linear visco-elastic damped wave models with a general time-dependent coefficient <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>g</mi>\u0000 <mo>=</mo>\u0000 <mi>g</mi>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$g=g(t)$</annotation>\u0000 </semantics></math>:\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4535-4581"},"PeriodicalIF":0.8,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300341","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860474","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 temporal regularity and polynomial decay of solutions for a class of nonlinear time-delayed fractional reaction–diffusion equations","authors":"Tran Thi Thu,&nbsp;Tran Van Tuan","doi":"10.1002/mana.202300434","DOIUrl":"https://doi.org/10.1002/mana.202300434","url":null,"abstract":"<p>This paper is devoted to analyzing the regularity in time and polynomial decay of solutions for a class of fractional reaction–diffusion equations (FrRDEs) involving delays and nonlinear perturbations in a bounded domain of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mo>R</mo>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <annotation>$operatorname{mathbf {R}}^{d}$</annotation>\u0000 </semantics></math>. By establishing some regularity estimates in both time and space variables of the resolvent operator, we present results on the Hölder and <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$C^{1}$</annotation>\u0000 </semantics></math>-regularity in time of solutions for both time-delayed linear and semilinear FrRDEs. Based on the aforementioned results, we study the existence, uniqueness, and regularity of solutions to an identification problem subjected to the delay FrRDE and the additional observations given at final time. Furthermore, under quite reasonable assumptions on nonlinear perturbations and the technique of measure of noncompactness, the existence of decay solutions with polynomial rates for the problem under consideration is shown.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4510-4534"},"PeriodicalIF":0.8,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860473","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":"Curves on Brill–Noether special K3 surfaces","authors":"Richard Haburcak","doi":"10.1002/mana.202300403","DOIUrl":"https://doi.org/10.1002/mana.202300403","url":null,"abstract":"<p>Mukai showed that projective models of Brill–Noether general polarized K3 surfaces of genus 6–10 and 12 are obtained as linear sections of projective homogeneous varieties, and that their hyperplane sections are Brill–Noether general curves. In general, the question, raised by Knutsen, and attributed to Mukai, of whether the Brill–Noether generality of any polarized K3 surface <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>S</mi>\u0000 <mo>,</mo>\u0000 <mi>H</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(S,H)$</annotation>\u0000 </semantics></math> is equivalent to the Brill–Noether generality of smooth curves <span></span><math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$C$</annotation>\u0000 </semantics></math> in the linear system <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>H</mi>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <annotation>$|H|$</annotation>\u0000 </semantics></math>, is still open. Using Lazarsfeld–Mukai bundle techniques, we answer this question in the affirmative for polarized K3 surfaces of genus <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>≤</mo>\u0000 <mn>19</mn>\u0000 </mrow>\u0000 <annotation>$le 19$</annotation>\u0000 </semantics></math>, which provides a new and unified proof even in the genera where Mukai models exist.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4497-4509"},"PeriodicalIF":0.8,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300403","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860472","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":"Boundary controllability of a Korteweg–de Vries-type Boussinesq system","authors":"Vilmos Komornik,&nbsp;Ademir F. Pazoto,&nbsp;Miguel D. Soto Vieira","doi":"10.1002/mana.202400201","DOIUrl":"https://doi.org/10.1002/mana.202400201","url":null,"abstract":"<p>The two-way propagation of a certain class of long-crested water waves is governed approximately by systems of equations of the Boussinesq type. These equations have been put forward in various forms by many authors and their higher-order generalizations arise when modeling the propagation of waves on large lakes, ocean, and in other contexts. Considered here is a class of such system which couple two higher-order Korteweg–de-Vries type equations. Our aim is to investigate the controllability properties of the linearized model posed on a periodic interval. By using the classical duality approach and some theorems on nonharmonic Fourier series, we prove that the system is exactly controllable in certain well-chosen Sobolev spaces by means of suitable boundary controls.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4478-4496"},"PeriodicalIF":0.8,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860037","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":"ε\u0000 $varepsilon$\u0000 -Regularity criteria and the number of singular points for the 3D simplified Ericksen–Leslie system","authors":"Zhongbao Zuo","doi":"10.1002/mana.202400071","DOIUrl":"https://doi.org/10.1002/mana.202400071","url":null,"abstract":"<p>In this paper, we consider the partial regularity of suitable weak solution to the 3D simplify Ericksen–Leslie system modeling the hydrodynamical motion of nematic liquid crystal flow, which is a coupled system with the Navier–Stokes equations for the velocity field and kinematic transport equations for the molecular orientation field. We present a new regularity criteria for suitable weak solutions to the 3D simplified Ericksen–Leslie system. Moreover, under the condition\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4370-4388"},"PeriodicalIF":0.8,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142859984","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}