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Logarithmic Hardy-Littlewood-Sobolev inequality on pseudo-Einstein 3-manifolds and the logarithmic Robin mass 伪爱因斯坦3-流形上的对数Hardy-Littlewood-Sobolev不等式和对数Robin质量
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2019-11-17 DOI: 10.5565/publmat6722302
Ali Maalaoui
{"title":"Logarithmic Hardy-Littlewood-Sobolev inequality on pseudo-Einstein 3-manifolds and the logarithmic Robin mass","authors":"Ali Maalaoui","doi":"10.5565/publmat6722302","DOIUrl":"https://doi.org/10.5565/publmat6722302","url":null,"abstract":"Given a three dimensional pseudo-Einstein CR manifold $(M,T^{1,0}M,theta)$, we study the existence of a contact structure conformal to $theta$ for which the logarithmic Hardy-Littlewood-Sobolev (LHLS) inequality holds. Our approach closely follows cite{Ok1} in the Riemannian setting. For this purpose, we introduce the notion of Robin mass as the constant term appearing in the expansion of the Green's function of the $P'$-operator. We show that the LHLS inequality appears when we study the variation of the total mass under conformal change. Then we exhibit an Aubin type result guaranteeing the existence of a minimizer for the total mass which yields the classical LHLS inequality.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47547179","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: 3
Coercivity for travelling waves in the Gross-Pitaevskii equation in $mathbb{R}^2$ for small speed 小速度下$mathbb｛R｝^2中Gross-Pitaevskii方程中行波的矫顽力
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2019-11-10 DOI: 10.5565/PUBLMAT6712307
D. Chiron, Eliot Pacherie
{"title":"Coercivity for travelling waves in the Gross-Pitaevskii equation in $mathbb{R}^2$ for small speed","authors":"D. Chiron, Eliot Pacherie","doi":"10.5565/PUBLMAT6712307","DOIUrl":"https://doi.org/10.5565/PUBLMAT6712307","url":null,"abstract":"In a previous paper, we constructed a smooth branch of travelling waves for the 2 dimensional Gross-Pitaevskii equation. Here, we continue the study of this branch. We show some coercivity results, and we deduce from them the kernel of the linearized operator, a spectral stability result, as well as a uniqueness result in the energy space.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42935441","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: 6
A small closed convex projective 4-manifold via Dehn filling 利用Dehn填充的闭凸投影4-流形
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2019-10-25 DOI: 10.5565/PUBLMAT6612215
Gye-Seon Lee, Ludovic Marquis, Stefano Riolo
{"title":"A small closed convex projective 4-manifold via Dehn filling","authors":"Gye-Seon Lee, Ludovic Marquis, Stefano Riolo","doi":"10.5565/PUBLMAT6612215","DOIUrl":"https://doi.org/10.5565/PUBLMAT6612215","url":null,"abstract":"In order to obtain a closed orientable convex projective four-manifold with small positive Euler characteristic, we build an explicit example of convex projective Dehn filling of a cusped hyperbolic four-manifold through a continuous path of projective cone-manifolds.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42112004","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: 2
Induced Hopf Galois structures and their local Hopf Galois modules 诱导Hopf伽罗瓦结构及其局部Hopf伽罗瓦模块
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2019-10-14 DOI: 10.5565/PUBLMAT6612204
Daniel Gil-Muñoz, A. Rio
{"title":"Induced Hopf Galois structures and their local Hopf Galois modules","authors":"Daniel Gil-Muñoz, A. Rio","doi":"10.5565/PUBLMAT6612204","DOIUrl":"https://doi.org/10.5565/PUBLMAT6612204","url":null,"abstract":"The regular subgroup determining an induced Hopf Galois structure for a Galois extension $L/K$ is obtained as the direct product of the corresponding regular groups of the inducing subextensions. We describe here the associated Hopf algebra and Hopf action of an induced structure and we prove that they are obtained by tensoring the corresponding inducing objects. In order to deal with their associated orders we develop a general method to compute bases and free generators in terms of matrices coming from representation theory of Hopf modules. In the case of an induced Hopf Galois structure it allows us to decompose the associated order, assuming that inducing subextensions are arithmetically disjoint.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42925188","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: 4
Stallings automata for free-times-abelian groups: intersections and index 自由时间阿贝尔群的Stallings自动机：交集和索引
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2019-10-13 DOI: 10.5565/publmat6622209
Jordi Delgado, E. Ventura
{"title":"Stallings automata for free-times-abelian groups: intersections and index","authors":"Jordi Delgado, E. Ventura","doi":"10.5565/publmat6622209","DOIUrl":"https://doi.org/10.5565/publmat6622209","url":null,"abstract":"We extend the classical Stallings theory (describing subgroups of free groups as automata) to direct products of free and abelian groups: after introducing enriched automata (i.e., automata with extra abelian labels), we obtain an explicit bijection between subgroups and a certain type of such enriched automata, which - as it happens in the free group - is computable in the finitely generated case. \u0000This approach provides a neat geometric description of (even non finitely generated) intersections of finitely generated subgroups within this non-Howson family. In particular, we give a geometric solution to the subgroup intersection problem and the finite index problem, providing recursive bases and transversals respectively.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44209732","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: 6
Iteration of functions and contractibility of acyclic 2-complexes 函数的迭代与无环2-配合物的可收缩性
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2019-10-02 DOI: 10.5565/publmat6512110
I. Leary
{"title":"Iteration of functions and contractibility of acyclic 2-complexes","authors":"I. Leary","doi":"10.5565/publmat6512110","DOIUrl":"https://doi.org/10.5565/publmat6512110","url":null,"abstract":"We show that there can be no algorithm to decide whether infinite recursively described acyclic aspherical 2-complexes are contractible. We construct such a complex that is contractible if and only if the Collatz conjecture holds.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42365727","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
Directional maximal function along the primes 沿素数方向的极大函数
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2019-09-29 DOI: 10.5565/PUBLMAT6522113
Laura Cladek, Polona Durcik, B. Krause, Jos'e Madrid
{"title":"Directional maximal function along the primes","authors":"Laura Cladek, Polona Durcik, B. Krause, Jos'e Madrid","doi":"10.5565/PUBLMAT6522113","DOIUrl":"https://doi.org/10.5565/PUBLMAT6522113","url":null,"abstract":"We study a two-dimensional discrete directional maximal operator along the set of the prime numbers. We show existence of a set of vectors, which are lattice points in a sufficiently large annulus, for which the $ell^2$ norm of the associated maximal operator with supremum taken over all large scales grows with an epsilon power in the number of vectors. This paper is a follow-up to a prior work on the discrete directional maximal operator along the integers by the first and third author.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46627777","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
Topologically semisimple and topologically perfect topological rings 拓扑半单拓扑环与拓扑完全拓扑环
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2019-09-26 DOI: 10.5565/PUBLMAT6622202
L. Positselski, J. Šťovíček
{"title":"Topologically semisimple and topologically perfect topological rings","authors":"L. Positselski, J. Šťovíček","doi":"10.5565/PUBLMAT6622202","DOIUrl":"https://doi.org/10.5565/PUBLMAT6622202","url":null,"abstract":"Extending the Wedderburn-Artin theory of (classically) semisimple associative rings to the realm of topological rings with right linear topology, we show that the abelian category of left contramodules over such a ring is split (equivalently, semisimple) if and only if the abelian category of discrete right modules over the same ring is split (equivalently, semisimple). An extension of the Bass theory of left perfect rings to the topological realm is formulated as a list of conjecturally equivalent conditions, some equivalences and implications between which we prove. Considering the rings of endomorphisms of modules as topological rings in the finite topology, we establish a close connection between the conjectural concept of a topologically perfect topological ring and the theory of modules with perfect decomposition. Our results also apply to endomorphism rings and direct sum decompositions of objects in certain additive categories more general than the categories of modules; we call them topologically agreeable categories. In particular, we show that a module $Sigma$-coperfect over its endomorphism ring has a perfect decomposition provided that the endomorphism ring is commutative, and that all countably indexed local direct summands are direct summands in any countably generated endo-$Sigma$-coperfect module.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42074313","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: 11
Relating second order geometry of manifolds through projections and normal sections 通过投影和法向截面联系流形的二阶几何
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2019-09-16 DOI: 10.5565/publmat6512114
P. B. Riul, R. O. Sinha
{"title":"Relating second order geometry of manifolds through projections and normal sections","authors":"P. B. Riul, R. O. Sinha","doi":"10.5565/publmat6512114","DOIUrl":"https://doi.org/10.5565/publmat6512114","url":null,"abstract":"We use normal sections to relate the curvature locus of regular (resp. singular corank 1) 3-manifolds in $mathbb{R}^6$ (resp. $mathbb R^5$) with regular (resp. singular corank 1) surfaces in $mathbb R^5$ (resp. $mathbb R^4$). For example we show how to generate a Roman surface by a family of ellipses different to Steiner's way. Furthermore, we give necessary conditions for the 2-jet of the parametrisation of a singular 3-manifold to be in a certain orbit in terms of the topological types of the curvature loci of the singular surfaces obtained as normal sections. We also study the relations between the regular and singular cases through projections. We show there is a commutative diagram of projections and normal sections which relates the curvature loci of the different types of manifolds, and therefore, that the second order geometry of all of them is related. In particular we define asymptotic directions for singular corank 1 3-manifolds in $mathbb R^5$ and relate them to asymptotic directions of regular 3-manifolds in $mathbb R^6$ and singular corank 1 surfaces in $mathbb R^4$.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46876389","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: 6
Locally countable pseudovarieties 局部可数的假变种
IF 1.1 3区 数学
Publicacions Matematiques Pub Date : 2019-09-11 DOI: 10.5565/PUBLMAT6712303
J. Almeida, O. Kl'ima
{"title":"Locally countable pseudovarieties","authors":"J. Almeida, O. Kl'ima","doi":"10.5565/PUBLMAT6712303","DOIUrl":"https://doi.org/10.5565/PUBLMAT6712303","url":null,"abstract":"The purpose of this paper is to contribute to the theory of profinite semigroups by considering the special class consisting of those all of whose finitely generated closed subsemigroups are countable, which are said to be locally countable. We also call locally countable a pseudovariety V (of finite semigroups) for which all pro-V semigroups are locally countable. We investigate operations preserving local countability of pseudovarieties and show that, in contrast with local finiteness, several natural operations do not preserve it. We also investigate the relationship of a finitely generated profinite semigroup being countable with every element being expressable in terms of the generators using multiplication and the idempotent (omega) power. The two properties turn out to be equivalent if there are only countably many group elements, gathered in finitely many regular J-classes. We also show that the pseudovariety generated by all finite ordered monoids satisfying the inequality $1le x^n$ is locally countable if and only if $n=1$.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44319357","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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