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Exponential localization in 2D pure magnetic wells 二维纯磁井的指数定位
IF 0.7 4区 数学
Arkiv for Matematik Pub Date : 2019-10-18 DOI: 10.4310/arkiv.2021.v59.n1.a3
Y. Bonthonneau, N. Raymond, San Vũ Ngọc
{"title":"Exponential localization in 2D pure magnetic wells","authors":"Y. Bonthonneau, N. Raymond, San Vũ Ngọc","doi":"10.4310/arkiv.2021.v59.n1.a3","DOIUrl":"https://doi.org/10.4310/arkiv.2021.v59.n1.a3","url":null,"abstract":"We establish a magnetic Agmon estimate in the case of a purely magnetic single non-degenerate well, by means of the Fourier-Bros-Iagolnitzer transform and microlocal exponential estimates a la Martinez-Sjostrand.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393664","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: 8
Topology change of level sets in Morse theory 莫尔斯理论中水平集的拓扑变化
IF 0.7 4区 数学
Arkiv for Matematik Pub Date : 2019-10-11 DOI: 10.4310/arkiv.2020.v58.n2.a6
A. Knauf, N. Martynchuk
{"title":"Topology change of level sets in Morse theory","authors":"A. Knauf, N. Martynchuk","doi":"10.4310/arkiv.2020.v58.n2.a6","DOIUrl":"https://doi.org/10.4310/arkiv.2020.v58.n2.a6","url":null,"abstract":"Classical Morse theory proceeds by considering sublevel sets $f^{-1}(-infty, a]$ of a Morse function $f: M to R$, where $M$ is a smooth finite-dimensional manifold. In this paper, we study the topology of the level sets $f^{-1}(a)$ and give conditions under which the topology of $f^{-1}(a)$ changes when passing a critical value. We show that for a general class of functions, which includes all exhaustive Morse function, the topology of a regular level $f^{-1}(a)$ always changes when passing a single critical point, unless the index of the critical point is half the dimension of the manifold $M$. When $f$ is a natural Hamiltonian on a cotangent bundle, we obtain more precise results in terms of the topology of the configuration space. (Counter-)examples and applications to celestial mechanics are also discussed.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393543","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
Weakly trapped submanifolds in standard static spacetimes 标准静态时空中的弱俘获子流形
IF 0.7 4区 数学
Arkiv for Matematik Pub Date : 2019-10-01 DOI: 10.4310/arkiv.2019.v57.n2.a4
A. Freitas, H. F. Lima, E. Lima, Márcio S. Santos
{"title":"Weakly trapped submanifolds in standard static spacetimes","authors":"A. Freitas, H. F. Lima, E. Lima, Márcio S. Santos","doi":"10.4310/arkiv.2019.v57.n2.a4","DOIUrl":"https://doi.org/10.4310/arkiv.2019.v57.n2.a4","url":null,"abstract":"We study weakly trapped submanifolds of codimension two in a standard static spacetime. In this setting, we apply some generalized maximum principles in order to investigate the geometry of these trapped submanifolds. For instance, we establish sufficient conditions to guarantee that such a spacelike submanifold must be a hypersurface of the Riemannian base of the ambient spacetime. As a consequence, we prove that there do not exist n-dimensional compact (without boundary) trapped submanifolds immersed in an (n+2)-dimensional standard static spacetime. Such a nonexistence result was originally obtained for stationary spacetimes by Mars and Senovilla [20]. Furthermore, we also investigate parabolic weakly trapped submanifolds immersed in a standard static spacetime.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393680","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
A reverse quasiconformal composition problem for $Q_alpha(mathbb{R}^n)$ $Q_alpha(mathbb{R}^n)$的逆拟共形复合问题
IF 0.7 4区 数学
Arkiv for Matematik Pub Date : 2019-10-01 DOI: 10.4310/arkiv.2019.v57.n2.a11
J. Xiao, Yuan Zhou
{"title":"A reverse quasiconformal composition problem for $Q_alpha(mathbb{R}^n)$","authors":"J. Xiao, Yuan Zhou","doi":"10.4310/arkiv.2019.v57.n2.a11","DOIUrl":"https://doi.org/10.4310/arkiv.2019.v57.n2.a11","url":null,"abstract":"","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393638","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
On the Hardy number of a domain in terms of harmonic measure and hyperbolic distance 关于调和测度和双曲距离的定义域哈代数
IF 0.7 4区 数学
Arkiv for Matematik Pub Date : 2019-08-30 DOI: 10.4310/arkiv.2020.v58.n2.a5
Christina Karafyllia
{"title":"On the Hardy number of a domain in terms of harmonic measure and hyperbolic distance","authors":"Christina Karafyllia","doi":"10.4310/arkiv.2020.v58.n2.a5","DOIUrl":"https://doi.org/10.4310/arkiv.2020.v58.n2.a5","url":null,"abstract":"Let $psi $ be a conformal map on $mathbb{D}$ with $ psi left( 0 right)=0$ and let ${F_alpha }=left{ {z in mathbb{D}:left| {psi left( z right)} right| = alpha } right}$ for $alpha >0$. Denote by ${H^p}left( mathbb{D} right)$ the classical Hardy space with exponent $p>0$ and by ${tt h}left( psi right)$ the Hardy number of $psi$. Consider the limits $$ L:= lim_{alphato+infty}left( log omega_{mathbb D}(0,F_{alpha})^{-1}/log alpha right), ,, mu:= lim_{alphato+infty}left( d_{mathbb D}(0,F_{alpha})/logalpha right),$$ where $omega _mathbb{D}left( {0,{F_alpha }} right)$ denotes the harmonic measure at $0$ of $F_alpha $ and $d_mathbb{D} {left( {0,{F_alpha }} right)}$ denotes the hyperbolic distance between $0$ and $F_alpha$ in $mathbb{D}$. We study a problem posed by P. Poggi-Corradini. What is the relation between $L$, $mu$ and ${tt h}left( psi right)$? We also provide conditions for the existence of $L$ and $mu$ and for the equalities $L=mu={tt h}left( psi right)$. Poggi-Corradini proved that $psi notin {H^{mu}}left( mathbb{D} right)$ for a wide class of conformal maps $psi$. We present an example of $psi$ such that $psi in {H^mu {left( mathbb{D} right)} }$.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393506","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: 9
Optimal unions of scaled copies of domains and Pólya's conjecture 域的缩放副本的最优联合和Pólya的猜想
IF 0.7 4区 数学
Arkiv for Matematik Pub Date : 2019-08-22 DOI: 10.4310/arkiv.2021.v59.n1.a2
P. Freitas, J. Lagac'e, Jordan Payette
{"title":"Optimal unions of scaled copies of domains and Pólya's conjecture","authors":"P. Freitas, J. Lagac'e, Jordan Payette","doi":"10.4310/arkiv.2021.v59.n1.a2","DOIUrl":"https://doi.org/10.4310/arkiv.2021.v59.n1.a2","url":null,"abstract":"Given a bounded Euclidean domain $Omega$, we consider the sequence of optimisers of the $k^{rm th}$ Laplacian eigenvalue within the family consisting of all possible disjoint unions of scaled copies of $Omega$ with fixed total volume. We show that this sequence encodes information yielding conditions for $Omega$ to satisfy Polya's conjecture with either Dirichlet or Neumann boundary conditions. This is an extension of a result by Colbois and El Soufi which applies only to the case where the family of domains consists of all bounded domains. Furthermore, we fully classify the different possible behaviours for such sequences, depending on whether Polya's conjecture holds for a given specific domain or not. This approach allows us to recover a stronger version of Polya's original results for tiling domains satisfying some dynamical billiard conditions, and a strenghtening of Urakawa's bound in terms of packing density.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393617","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: 3
The doubling metric and doubling measures 加倍度量和加倍度量
IF 0.7 4区 数学
Arkiv for Matematik Pub Date : 2019-08-20 DOI: 10.4310/arkiv.2020.v58.n2.a2
J. Flesch, A. Predtetchinski, Ville Suomala
{"title":"The doubling metric and doubling measures","authors":"J. Flesch, A. Predtetchinski, Ville Suomala","doi":"10.4310/arkiv.2020.v58.n2.a2","DOIUrl":"https://doi.org/10.4310/arkiv.2020.v58.n2.a2","url":null,"abstract":"We introduce the so--called doubling metric on the collection of non--empty bounded open subsets of a metric space. Given a subset $U$ of a metric space $X$, the predecessor $U_{*}$ of $U$ is defined by doubling the radii of all open balls contained inside $U$, and taking their union. If $U$ is open, the predecessor of $U$ is an open set containing $U$. The directed doubling distance between $U$ and another subset $V$ is the number of times that the predecessor operation needs to be applied to $U$ to obtain a set that contains $V$. Finally, the doubling distance between $U$ and $V$ is the maximum of the directed distance between $U$ and $V$ and the directed distance between $V$ and $U$.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47580501","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
On Laplace–Carleson embeddings, and $L^p$-mapping properties of the Fourier transform 关于拉普拉斯-卡尔森嵌入，以及傅里叶变换的L^p -映射性质
IF 0.7 4区 数学
Arkiv for Matematik Pub Date : 2019-07-26 DOI: 10.4310/arkiv.2020.v58.n2.a10
E. Rydhe
{"title":"On Laplace–Carleson embeddings, and $L^p$-mapping properties of the Fourier transform","authors":"E. Rydhe","doi":"10.4310/arkiv.2020.v58.n2.a10","DOIUrl":"https://doi.org/10.4310/arkiv.2020.v58.n2.a10","url":null,"abstract":"We investigate so-called Laplace--Carleson embeddings for large exponents. In particular, we extend some results by Jacob, Partington, and Pott. We also discuss some related results for Sobolev- and Besov spaces, and mapping properties of the Fourier transform. These variants of the Hausdorff--Young theorem appear difficult to find in the literature. We conclude the paper with an example related to an open problem.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393442","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: 6
Sufficient and necessary conditions for local rigidity of CR mappings and higher order infinitesimal deformations CR映射局部刚度和高阶无穷小变形的充要条件
IF 0.7 4区 数学
Arkiv for Matematik Pub Date : 2019-06-06 DOI: 10.4310/ARKIV.2020.v58.n2.a1
G. Sala, B. Lamel, M. Reiter
{"title":"Sufficient and necessary conditions for local rigidity of CR mappings and higher order infinitesimal deformations","authors":"G. Sala, B. Lamel, M. Reiter","doi":"10.4310/ARKIV.2020.v58.n2.a1","DOIUrl":"https://doi.org/10.4310/ARKIV.2020.v58.n2.a1","url":null,"abstract":"In this paper we continue our study of local rigidity for maps of CR submanifolds of the complex space. We provide a linear sufficient condition for local rigidity of finitely nondegenerate maps between minimal CR manifolds. Furthermore, we show higher order infinitesimal conditions can be used to give a characterization of local rigidity.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47544624","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: 3
The Lelong number, the Monge–Ampère mass, and the Schwarz symmetrization of plurisubharmonic functions Lelong数，monge - ampantere质量，和多重次谐波函数的Schwarz对称
IF 0.7 4区 数学
Arkiv for Matematik Pub Date : 2019-05-25 DOI: 10.4310/arkiv.2020.v58.n2.a8
Long Li
{"title":"The Lelong number, the Monge–Ampère mass, and the Schwarz symmetrization of plurisubharmonic functions","authors":"Long Li","doi":"10.4310/arkiv.2020.v58.n2.a8","DOIUrl":"https://doi.org/10.4310/arkiv.2020.v58.n2.a8","url":null,"abstract":"The aim of this paper is to study the Lelong number, the integrability index and the Monge-Ampere mass at the origin of an $S^1$-invariant plurisubharmonic function on a balanced domain in $mathbb{C}^n$ under the Schwarz symmetrization. We prove that $n$ times the integrability index is exactly the Lelong number of the symmetrization, and if the function is further toric with a single pole at the origin, then the Monge-Ampere mass is always decreasing under the symmetrization","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393599","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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