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Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg最新文献

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A Brunn–Minkowski type inequality for extended symplectic capacities of convex domains and length estimate for a class of billiard trajectories 一类弹子轨迹凸域扩展辛容量的Brunn-Minkowski型不等式及长度估计
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2023-02-23 DOI: 10.1007/s12188-023-00263-z
Rongrong Jin, Guangcun Lu
{"title":"A Brunn–Minkowski type inequality for extended symplectic capacities of convex domains and length estimate for a class of billiard trajectories","authors":"Rongrong Jin,&nbsp;Guangcun Lu","doi":"10.1007/s12188-023-00263-z","DOIUrl":"10.1007/s12188-023-00263-z","url":null,"abstract":"<div><p>In this paper, we firstly generalize the Brunn–Minkowski type inequality for Ekeland–Hofer–Zehnder symplectic capacity of bounded convex domains established by Artstein-Avidan–Ostrover in 2008 to extended symplectic capacities of bounded convex domains constructed by authors based on a class of Hamiltonian non-periodic boundary value problems recently. Then we introduce a class of non-periodic billiards in convex domains, and for them we prove some corresponding results to those for periodic billiards in convex domains obtained by Artstein-Avidan–Ostrover in 2012.\u0000</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"93 1","pages":"1 - 30"},"PeriodicalIF":0.4,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50043772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Picard schemes of noncommutative bielliptic surfaces 非交换双椭圆曲面的Picard格式
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2023-02-14 DOI: 10.1007/s12188-023-00265-x
Fabian Reede
{"title":"Picard schemes of noncommutative bielliptic surfaces","authors":"Fabian Reede","doi":"10.1007/s12188-023-00265-x","DOIUrl":"10.1007/s12188-023-00265-x","url":null,"abstract":"<div><p>We study the nontrivial elements in the Brauer group of a bielliptic surface and show that they can be realized as Azumaya algebras with a simple structure at the generic point of the surface. We go on to study some properties of the noncommutative Picard scheme associated to such an Azumaya algebra.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"93 1","pages":"61 - 70"},"PeriodicalIF":0.4,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-023-00265-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50026242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence and uniqueness of renormalized solutions for initial boundary value parabolic problems with possibly very singular right-hand side 可能有非常奇异的初始边值抛物型问题重整解的存在唯一性
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-12-13 DOI: 10.1007/s12188-022-00262-6
M. Abdellaoui, H. Redwane
{"title":"Existence and uniqueness of renormalized solutions for initial boundary value parabolic problems with possibly very singular right-hand side","authors":"M. Abdellaoui,&nbsp;H. Redwane","doi":"10.1007/s12188-022-00262-6","DOIUrl":"10.1007/s12188-022-00262-6","url":null,"abstract":"<div><p>We study the existence and uniqueness of <i>renormalized</i> solutions for initial boundary value problems of the type </p><div><div><span>$$begin{aligned} left( {mathcal {P}}_{b}^{1}right) quad left{ begin{aligned} u_{t}-text {div}(a(t,x,nabla u))=H(u)mu text { in }Q:=(0,T)times Omega , u(0,x)=u_{0}(x)text { in }Omega , u(t,x)=0text { on }(0,T)times partial Omega , end{aligned}right. end{aligned}$$</span></div></div><p>where <span>(u_{0}in L^{1}(Omega ))</span>, <span>(mu in {mathcal {M}}_{b}(Q))</span> is a general <i>Radon</i> measure on <i>Q</i> and <span>(Hin C_{b}^{0}({mathbb {R}}))</span> is a continuous positive bounded function on <span>({mathbb {R}})</span>. The difficulties in the study of such problems concern the possibly very singular right-hand side that forces the choice of a suitable formulation that ensures both existence and uniqueness of solution. Using similar techniques, we will prove existence/nonexistence results of the auxiliary problem </p><div><div><span>$$begin{aligned} left( {mathcal {P}}_{b}^{2}right) quad left{ begin{aligned}&amp;u_{t}-text {div}(a(t,x,nabla u))+g(x,u)|nabla u|^{2}=mu text { in }Q:=(0,T)times Omega ,&amp;u(0,x)=u_{0}(x)text { in }Omega , u(t,x)=0text { on }(0,T)times partial Omega , end{aligned}right. end{aligned}$$</span></div></div><p>under the assumption that <i>g</i> satisfies a sign condition and the nonlinear term depends on both <i>x</i>, <i>u</i> and its gradient. Thus, our results improve and complete the previous known existence results for problems <span>(left( {mathcal {P}}_{b}^{1,2}right) )</span>.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"92 2","pages":"209 - 245"},"PeriodicalIF":0.4,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50023054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A tree-of-tangles theorem for infinite tangles 关于无穷多个纠缠的一个纠缠树定理
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-11-29 DOI: 10.1007/s12188-022-00259-1
Ann-Kathrin Elm, Jan Kurkofka
{"title":"A tree-of-tangles theorem for infinite tangles","authors":"Ann-Kathrin Elm,&nbsp;Jan Kurkofka","doi":"10.1007/s12188-022-00259-1","DOIUrl":"10.1007/s12188-022-00259-1","url":null,"abstract":"<div><p>Carmesin has extended Robertson and Seymour’s tree-of-tangles theorem to the infinite tangles of locally finite infinite graphs. We extend it further to the infinite tangles of all infinite graphs. Our result has a number of applications for the topology of infinite graphs, such as their end spaces and their compactifications.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"92 2","pages":"139 - 178"},"PeriodicalIF":0.4,"publicationDate":"2022-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-022-00259-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50104037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
(G_2)-structures on flat solvmanifolds (G_2)平面溶剂流形上的结构
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-11-11 DOI: 10.1007/s12188-022-00261-7
Alejandro Tolcachier
{"title":"(G_2)-structures on flat solvmanifolds","authors":"Alejandro Tolcachier","doi":"10.1007/s12188-022-00261-7","DOIUrl":"10.1007/s12188-022-00261-7","url":null,"abstract":"<div><p>In this article we study the relation between flat solvmanifolds and <span>(G_2)</span>-geometry. First, we give a classification of 7-dimensional flat splittable solvmanifolds using the classification of finite subgroups of <span>(mathsf{GL}(n,mathbb {Z}))</span> for <span>(n=5)</span> and <span>(n=6)</span>. Then, we look for closed, coclosed and divergence-free <span>(G_2)</span>-structures compatible with the flat metric on them. In particular, we provide explicit examples of compact flat manifolds with a torsion-free <span>(G_2)</span>-structure whose finite holonomy is cyclic and contained in <span>(G_2)</span>, and examples of compact flat manifolds admitting a divergence-free <span>(G_2)</span>-structure.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"92 2","pages":"179 - 207"},"PeriodicalIF":0.4,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50020079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Local positivity and effective Diophantine approximation 局部正性和有效丢番图近似
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-11-08 DOI: 10.1007/s12188-022-00260-8
Matthias Nickel
{"title":"Local positivity and effective Diophantine approximation","authors":"Matthias Nickel","doi":"10.1007/s12188-022-00260-8","DOIUrl":"10.1007/s12188-022-00260-8","url":null,"abstract":"<div><p>In this paper we present a new approach to prove effective results in Diophantine approximation. This approach involves measures of local positivity of divisors combined with Faltings’s version of Siegel’s lemma instead of a zero estimate such as Dyson’s lemma. We then use it to prove an effective theorem on the simultaneous approximation of two algebraic numbers satisfying an algebraic equation with complex coefficients.\u0000</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"92 2","pages":"125 - 138"},"PeriodicalIF":0.4,"publicationDate":"2022-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-022-00260-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50015028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On linear stability and syzygy stability 关于线性稳定性和系统稳定性
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-05-30 DOI: 10.1007/s12188-022-00258-2
Abel Castorena, Ernesto C. Mistretta, Hugo Torres-López
{"title":"On linear stability and syzygy stability","authors":"Abel Castorena,&nbsp;Ernesto C. Mistretta,&nbsp;Hugo Torres-López","doi":"10.1007/s12188-022-00258-2","DOIUrl":"10.1007/s12188-022-00258-2","url":null,"abstract":"<div><p>In previous works, the authors investigated the relationships between linear stability of a generated linear series |<i>V</i>| on a curve <i>C</i>, and slope stability of the syzygy vector bundle <span>(M_{V,L} := ker (V otimes mathcal {O}_C rightarrow L))</span>. In particular, the second named author and L. Stoppino conjecture that, for a complete linear system |<i>L</i>|, linear (semi)stability is equivalent to slope (semi)stability of <span>(M_{L})</span>. The first and third named authors proved that this conjecture holds in the two opposite cases: hyperelliptic and generic curves. In this work we provide a counterexample to this conjecture on any smooth plane curve of degree 7.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"92 1","pages":"91 - 103"},"PeriodicalIF":0.4,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-022-00258-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50104289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Triangular lat-igusa-todorov algebras 三角lat-igusa-todorov代数
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-05-24 DOI: 10.1007/s12188-022-00257-3
José Armando Vivero
{"title":"Triangular lat-igusa-todorov algebras","authors":"José Armando Vivero","doi":"10.1007/s12188-022-00257-3","DOIUrl":"10.1007/s12188-022-00257-3","url":null,"abstract":"<div><p>In 2021 the authors D. Bravo, M. Lanzilotta, O. Mendoza and J. Vivero gave a generalization of the concept of Igusa-Todorov algebra and proved that those algebras, named Lat-Igusa-Todorov (LIT for short), satisfy the finitistic dimension conjecture. In this paper we explore the scope of that generalization and give conditions for a triangular matrix algebra to be LIT in terms of the algebras and the bimodule used in its definition. As an application we obtain that the tensor product of an LIT <span>(mathbb {K})</span>-algebra with a path algebra of a quiver whose underlying graph is a tree, is LIT.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"92 1","pages":"53 - 67"},"PeriodicalIF":0.4,"publicationDate":"2022-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50102451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Derivatives of Eisenstein series of weight 2 and intersections of modular correspondences 权值2的爱森斯坦级数的导数和模对应的交点
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-04-27 DOI: 10.1007/s12188-022-00256-4
Sungmun Cho, Shunsuke Yamana, Takuya Yamauchi
{"title":"Derivatives of Eisenstein series of weight 2 and intersections of modular correspondences","authors":"Sungmun Cho,&nbsp;Shunsuke Yamana,&nbsp;Takuya Yamauchi","doi":"10.1007/s12188-022-00256-4","DOIUrl":"10.1007/s12188-022-00256-4","url":null,"abstract":"<div><p>We give a formula for certain values and derivatives of Siegel series and use them to compute Fourier coefficients of derivatives of the Siegel Eisenstein series of weight <span>(frac{g}{2})</span> and genus <i>g</i>. When <span>(g=4)</span>, the Fourier coefficient is approximated by a certain Fourier coefficient of the central derivative of the Siegel Eisenstein series of weight 2 and genus 3, which is related to the intersection of 3 arithmetic modular correspondences. Applications include a relation between weighted averages of representation numbers of symmetric matrices.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"92 1","pages":"27 - 52"},"PeriodicalIF":0.4,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-022-00256-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50049460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Fourier coefficients of the Siegel Eisenstein series of degree 2 with odd prime level, corresponding to the middle cusp 具有奇数素数阶的2次西格尔-爱森斯坦级数的傅里叶系数，对应于中间尖
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-01-18 DOI: 10.1007/s12188-021-00255-x
Keiichi Gunji
{"title":"Fourier coefficients of the Siegel Eisenstein series of degree 2 with odd prime level, corresponding to the middle cusp","authors":"Keiichi Gunji","doi":"10.1007/s12188-021-00255-x","DOIUrl":"10.1007/s12188-021-00255-x","url":null,"abstract":"<div><p>Let <i>p</i> be an odd prime. In this paper we compute the Fourier coefficients of the Siegel Eisenstein series of degree 2, level <i>p</i> with the trivial or the quadratic character, associated to a certain cusp. For that we need to define the <i>p</i>-factor of the special type of Siegel series with character.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"92 1","pages":"69 - 83"},"PeriodicalIF":0.4,"publicationDate":"2022-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50036105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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