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Groups Acting on Moduli Spaces of Hyper-Kähler Manifolds 作用于超凯勒方程模空间的群
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-05-08 DOI: 10.1007/s00032-024-00396-7
Francesca Rizzo
{"title":"Groups Acting on Moduli Spaces of Hyper-Kähler Manifolds","authors":"Francesca Rizzo","doi":"10.1007/s00032-024-00396-7","DOIUrl":"https://doi.org/10.1007/s00032-024-00396-7","url":null,"abstract":"<p>The period morphism of polarized hyper-Kähler manifolds of K3<span>(^{[m]})</span>-type gives an embedding of each connected component of the moduli space of polarized hyper-Kähler manifolds of K3<span>(^{[m]})</span>-type into their period space, which is the quotient of a Hermitian symmetric domain by an arithmetic group. Following work of Stellari and Gritsenko-Hulek-Sankaran, we study the ramification of covering maps between these period spaces that arise from the action of some groups of isometries.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888716","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}
引用次数: 0
On the Existence and Partial Stability of Standing Waves for a Nematic Liquid Crystal Director Field Equations 论向列液晶导演场方程驻波的存在和部分稳定性
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-04-24 DOI: 10.1007/s00032-024-00395-8
Paulo Amorim, Jean-Baptiste Casteras, J. Dias
{"title":"On the Existence and Partial Stability of Standing Waves for a Nematic Liquid Crystal Director Field Equations","authors":"Paulo Amorim, Jean-Baptiste Casteras, J. Dias","doi":"10.1007/s00032-024-00395-8","DOIUrl":"https://doi.org/10.1007/s00032-024-00395-8","url":null,"abstract":"","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140662522","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}
引用次数: 0
On the Transport of Currents 论水流的传输
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-04-13 DOI: 10.1007/s00032-024-00394-9
Paolo Bonicatto
{"title":"On the Transport of Currents","authors":"Paolo Bonicatto","doi":"10.1007/s00032-024-00394-9","DOIUrl":"https://doi.org/10.1007/s00032-024-00394-9","url":null,"abstract":"<p>In this work, we consider some evolutionary models for <i>k</i>-currents in <span>(mathbb {R}^d)</span>. We study a transport-type equation which can be seen as a generalisation of the transport/continuity equation and can be used to model the movement of singular structures in a medium, such as vortex points/lines/sheets in fluids or dislocation loops in crystals. We provide a detailed overview of recent results on this equation obtained mostly in (Bonicatto et al. Transport of currents and geometric Rademacher-type theorems. arXiv:2207.03922, 2022; Bonicatto et al. Existence and uniqueness for the transport of currents by Lipschitz vector fields. arXiv:2303.03218, 2023). We work within the setting of integral (sometimes merely normal) <i>k</i>-currents, covering in particular existence and uniqueness of solutions, structure theorems, rectifiability, and a number of Rademacher-type differentiability results. These differentiability results are sharp and can be formulated in terms of a novel condition we called “Negligible Criticality condition” (NC), which turns out to be related also to Sard’s Theorem. We finally provide a new stability result for integral currents satisfying (NC) in a uniform way.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140596639","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}
引用次数: 0
The $$H^infty $$ -Functional Calculi for the Quaternionic Fine Structures of Dirac Type 狄拉克型四元精细结构的 $$H^infty $$ 函数计算
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-03-06 DOI: 10.1007/s00032-024-00392-x
Fabrizio Colombo, Stefano Pinton, Peter Schlosser
{"title":"The $$H^infty $$ -Functional Calculi for the Quaternionic Fine Structures of Dirac Type","authors":"Fabrizio Colombo, Stefano Pinton, Peter Schlosser","doi":"10.1007/s00032-024-00392-x","DOIUrl":"https://doi.org/10.1007/s00032-024-00392-x","url":null,"abstract":"<p>In recent works, various integral representations have been proposed for specific sets of functions. These representations are derived from the Fueter–Sce extension theorem, considering all possible factorizations of the Laplace operator in relation to both the Cauchy–Fueter operator (often referred to as the Dirac operator) and its conjugate. The collection of these function spaces, along with their corresponding functional calculi, are called the quaternionic fine structures within the context of the <i>S</i>-spectrum. In this paper, we utilize these integral representations of functions to introduce novel functional calculi tailored for quaternionic operators of sectorial type. Specifically, by leveraging the aforementioned factorization of the Laplace operator, we identify four distinct classes of functions: slice hyperholomorphic functions (leading to the <i>S</i>-functional calculus), axially harmonic functions (leading to the <i>Q</i>-functional calculus), axially polyanalytic functions of order 2 (leading to the <span>(P_2)</span>-functional calculus), and axially monogenic functions (leading to the <i>F</i>-functional calculus). By applying the respective product rule, we establish the four different <span>(H^infty )</span>-versions of these functional calculi.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140045488","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}
引用次数: 0
On the Automorphism Groups of Certain Branched Structures on Surfaces 论曲面上某些分支结构的自形群
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-02-14 DOI: 10.1007/s00032-024-00393-w
{"title":"On the Automorphism Groups of Certain Branched Structures on Surfaces","authors":"","doi":"10.1007/s00032-024-00393-w","DOIUrl":"https://doi.org/10.1007/s00032-024-00393-w","url":null,"abstract":"<h3>Abstract</h3> <p>We consider translation surfaces with poles on surfaces. We shall prove that any finite group appears as the automorphism group of some translation surface with poles. As a direct consequence we obtain the existence of structures achieving the maximal possible number of automorphisms allowed by their genus and we finally extend the same results to branched projective structures.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139767777","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}
引用次数: 0
Leray–Lions Equations of (p, q)-Type in the Entire Space with Unbounded Potentials 整个空间中的无界势能 (p, q) 型勒雷狮子方程
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-02-11 DOI: 10.1007/s00032-024-00391-y
Federica Mennuni, Dimitri Mugnai
{"title":"Leray–Lions Equations of (p, q)-Type in the Entire Space with Unbounded Potentials","authors":"Federica Mennuni, Dimitri Mugnai","doi":"10.1007/s00032-024-00391-y","DOIUrl":"https://doi.org/10.1007/s00032-024-00391-y","url":null,"abstract":"<p>In this paper we prove the existence of signed bounded solutions for a quasilinear elliptic equation in <span>({mathbb {R}}^N)</span> driven by a Leray–Lions operator of (<i>p</i>, <i>q</i>)–type in presence of unbounded potentials. A direct approach seems to be a hard task, and for this reason we will study approximating problems in bounded domains, whose resolutions needs refined tools from nonlinear analysis. In particular, we will use a weaker version of the classical Cerami–Palais–Smale condition together with a extension of the Weierstrass Theorem due to Candela–Palmieri, as well as a generalization of a celebrated convergence result by Boccardo–Murat–Puel.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139767761","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}
引用次数: 0
Deficiency Indices for Singular Magnetic Schrödinger Operators 奇异磁薛定谔算子的缺陷指数
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2024-01-08 DOI: 10.1007/s00032-023-00390-5
Michele Correggi, Davide Fermi
{"title":"Deficiency Indices for Singular Magnetic Schrödinger Operators","authors":"Michele Correggi, Davide Fermi","doi":"10.1007/s00032-023-00390-5","DOIUrl":"https://doi.org/10.1007/s00032-023-00390-5","url":null,"abstract":"<p>We show that the deficiency indices of magnetic Schrödinger operators with several local singularities can be computed in terms of the deficiency indices of operators carrying just one singularity each. We discuss some applications to physically relevant operators.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139413164","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}
引用次数: 0
Another Look at Elliptic Homogenization 对椭圆均匀化的另一个看法
IF 1.7 3区 数学
Milan Journal of Mathematics Pub Date : 2023-12-03 DOI: 10.1007/s00032-023-00389-y
Andrea Braides, Giuseppe Cosma Brusca, Davide Donati
{"title":"Another Look at Elliptic Homogenization","authors":"Andrea Braides, Giuseppe Cosma Brusca, Davide Donati","doi":"10.1007/s00032-023-00389-y","DOIUrl":"https://doi.org/10.1007/s00032-023-00389-y","url":null,"abstract":"<p>We consider the limit of sequences of normalized (<i>s</i>, 2)-Gagliardo seminorms with an oscillating coefficient as <span>(srightarrow 1)</span>. In a seminal paper by Bourgain et al. (Another look at Sobolev spaces. In: Optimal control and partial differential equations. IOS, Amsterdam, pp 439–455, 2001) it is proven that if the coefficient is constant then this sequence <span>(Gamma )</span>-converges to a multiple of the Dirichlet integral. Here we prove that, if we denote by <span>(varepsilon )</span> the scale of the oscillations and we assume that <span>(1-s&lt;!&lt;varepsilon ^2)</span>, this sequence converges to the homogenized functional formally obtained by separating the effects of <i>s</i> and <span>(varepsilon )</span>; that is, by the homogenization as <span>(varepsilon rightarrow 0)</span> of the Dirichlet integral with oscillating coefficient obtained by formally letting <span>(srightarrow 1)</span> first.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495300","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}
引用次数: 1
On the Dynamics of Aeolian Sand Ripples 风成沙波纹动力学研究
3区 数学
Milan Journal of Mathematics Pub Date : 2023-10-26 DOI: 10.1007/s00032-023-00388-z
Giuseppe Maria Coclite, Lorenzo di Ruvo
{"title":"On the Dynamics of Aeolian Sand Ripples","authors":"Giuseppe Maria Coclite, Lorenzo di Ruvo","doi":"10.1007/s00032-023-00388-z","DOIUrl":"https://doi.org/10.1007/s00032-023-00388-z","url":null,"abstract":"Abstract The dynamics of aeolian sand ripples is described by a 1D non-linear evolutive fourth order equation. In this paper, we prove the well-posedness of the classical solutions of the Cauchy problem, associated with this equation.","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134908601","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}
引用次数: 0
Correction to: Positive Solutions for Slightly Subcritical Elliptic Problems Via Orlicz Spaces 对略次临界椭圆型问题经Orlicz空间正解的修正
3区 数学
Milan Journal of Mathematics Pub Date : 2023-09-23 DOI: 10.1007/s00032-023-00386-1
Mabel Cuesta, Rosa Pardo
{"title":"Correction to: Positive Solutions for Slightly Subcritical Elliptic Problems Via Orlicz Spaces","authors":"Mabel Cuesta, Rosa Pardo","doi":"10.1007/s00032-023-00386-1","DOIUrl":"https://doi.org/10.1007/s00032-023-00386-1","url":null,"abstract":"","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135959263","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}
引用次数: 0
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