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Annales De L Institut Fourier最新文献

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On the spectral theory and dynamics of asymptotically hyperbolic manifolds 渐近双曲流形的谱理论与动力学
IF 0.7 4区 数学
Annales De L Institut Fourier Pub Date : 2020-12-11 DOI: 10.5802/aif.2615
Julie Rowlett
{"title":"On the spectral theory and dynamics of asymptotically hyperbolic manifolds","authors":"Julie Rowlett","doi":"10.5802/aif.2615","DOIUrl":"https://doi.org/10.5802/aif.2615","url":null,"abstract":"— We present a brief survey of the spectral theory and dynamics of infinite volume asymptotically hyperbolic manifolds. Beginning with their geometry and examples, we proceed to their spectral and scattering theories, dynamics, and the physical description of their quantum and classical mechanics. We conclude with a discussion of recent results, ideas, and conjectures. Resume. — Cet article est une presentation rapide de la theorie spectrale et de la dynamique des varietes asymptotiquement hyperboliques a volume infini. Nous commencons par leur geometrie et quelques exemples, nous poursuivons en rappelant leur theorie spectrale, puis continuons sur des developpements recents de leur dynamique. Nous concluons par une discussion des resultats qui demontrent un rapport entre leurs mecaniques quantiques et classiques et enfin, nous offrons quelques idees et conjectures.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45064382","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
Well-posedness for the Boussinesq system in critical spaces via maximal regularity 基于极大正则性的Boussinesq系统在临界空间中的适定性
IF 0.7 4区 数学
Annales De L Institut Fourier Pub Date : 2020-12-03 DOI: 10.5802/aif.3523
L. Brandolese, Sylvie Monniaux
{"title":"Well-posedness for the Boussinesq system in critical spaces via maximal regularity","authors":"L. Brandolese, Sylvie Monniaux","doi":"10.5802/aif.3523","DOIUrl":"https://doi.org/10.5802/aif.3523","url":null,"abstract":"We establish the existence and the uniqueness for the Boussinesq system in the whole 3D space in the critical space of continuous in time with values in the power 3 integrable in space functions for the velocity and square integrable in time with values in the power 3/2 integrable in space.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46288172","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: 4
Trivializations of moment maps 矩映射的琐碎化
IF 0.7 4区 数学
Annales De L Institut Fourier Pub Date : 2020-10-16 DOI: 10.5802/aif.3587
Mathieu Ballandras
{"title":"Trivializations of moment maps","authors":"Mathieu Ballandras","doi":"10.5802/aif.3587","DOIUrl":"https://doi.org/10.5802/aif.3587","url":null,"abstract":"We study various trivializations of moment maps. First in the general framework of a reductive group $G$ acting on a smooth affine variety. We prove that the moment map is a locally trivial fibration over a regular locus of the center of the Lie algebra of $H$ a maximal compact subgroup of $G$. The construction relies on Kempf-Ness theory and Morse theory of the square norm of the moment map studied by Kirwan, Ness-Mumford and Sjamaar. Then we apply it together with ideas from Nakajima and Kronheimer to trivialize the hyperkaehler moment map for Nakajima quiver varieties. Notice this trivialization result about quiver varieties was known and used by experts such as Nakajima and Maffei but we could not locate a proof in the literature.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42188770","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
Semiclassical Gevrey operators in the complex domain 复域上的半经典Gevrey算子
IF 0.7 4区 数学
Annales De L Institut Fourier Pub Date : 2020-09-19 DOI: 10.5802/aif.3546
M. Hitrik, R. Lascar, J. Sjoestrand, Maher Zerzeri
{"title":"Semiclassical Gevrey operators in the complex domain","authors":"M. Hitrik, R. Lascar, J. Sjoestrand, Maher Zerzeri","doi":"10.5802/aif.3546","DOIUrl":"https://doi.org/10.5802/aif.3546","url":null,"abstract":"We study semiclassical Gevrey pseudodifferential operators, acting on exponentially weighted spaces of entire holomorphic functions. The symbols of such operators are Gevrey functions defined on suitable I-Lagrangian submanifolds of the complexified phase space, which are extended almost holomorphically in the same Gevrey class, or in some larger space, to complex neighborhoods of these submanifolds. Using almost holomorphic extensions, we obtain uniformly bounded realizations of such operators on a natural scale of exponentially weighted spaces of holomorphic functions for all Gevrey indices, with remainders that are optimally small, provided that the Gevrey index is $leq 2$.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71210748","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: 4
Abelianization of some groups of interval exchanges 区间交换若干群的阿贝尔化
IF 0.7 4区 数学
Annales De L Institut Fourier Pub Date : 2020-09-16 DOI: 10.5802/aif.3466
Octave Lacourte
{"title":"Abelianization of some groups of interval exchanges","authors":"Octave Lacourte","doi":"10.5802/aif.3466","DOIUrl":"https://doi.org/10.5802/aif.3466","url":null,"abstract":"Let IET be the group of bijections from $mathopen{[}0,1 mathclose{[}$ to itself that are continuous outside a finite set, right-continuous and piecewise translations. The abelianization homomorphism $f: text{IET} to A$, called SAF-homomorphism, was described by Arnoux-Fathi and Sah. The abelian group $A$ is the second exterior power of the reals over the rationals. For every subgroup $Gamma$ of $mathbb{R/Z}$ we define $text{IET}(Gamma)$ as the subgroup of $text{IET}$ consisting of all elements $f$ such that $f$ is continuous outside $Gamma$. Let $tilde{Gamma}$ be the preimage of $Gamma$ in $mathbb{R}$. We establish an isomorphism between the abelianization of $text{IET}(Gamma)$ and the second skew-symmetric power of $tilde{Gamma}$ over $mathbb{Z}$ denoted by ${}^circleddash!!bigwedge^2_{mathbb{Z}} tilde{Gamma}$. This group often has non-trivial $2$-torsion, which is not detected by the SAF-homomorphism. We then define $text{IET}^{bowtie}$ the group of all interval exchange transformations with flips. Arnoux proved that this group is simple thus perfect. However for every subgroup $text{IET}^{bowtie}(Gamma)$ we establish an isomorphism between its abelianization and $langle lbrace a otimes a ~ [text{mod}~2] mid a in tilde{Gamma} rbrace rangle times langle lbrace ell wedge ell ~ [text{mod}~2] mid ell in tilde{Gamma} rbrace rangle$ which is a $2$-elementary abelian subgroup of $bigotimes^2_{mathbb{Z}} tilde{Gamma} / (2bigotimes^2_{mathbb{Z}} tilde{Gamma}) times {}^circleddash!!bigwedge^2_{mathbb{Z}} tilde{Gamma} / (2 {}^circleddash!!bigwedge^2_{mathbb{Z}} tilde{Gamma})$.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44773182","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
Prescription de courbure des feuilles des laminations : retour sur un théorème de Candel 轧制薄板曲率的规定:回到Candel定理
IF 0.7 4区 数学
Annales De L Institut Fourier Pub Date : 2020-09-09 DOI: 10.5802/aif.3476
Sébastien Alvarez, G. Smith
{"title":"Prescription de courbure des feuilles des laminations : retour sur un théorème de Candel","authors":"Sébastien Alvarez, G. Smith","doi":"10.5802/aif.3476","DOIUrl":"https://doi.org/10.5802/aif.3476","url":null,"abstract":"In the present paper, we revisit a famous theorem by Candel that we generalize by proving that given a compact lamination by hyperbolic surfaces, every negative function smooth inside the leaves and transversally continuous is the curvature function of a unique laminated metric in the corresponding conformal class. We give an interpretation of this result as a continuity result about the solutions of some elliptic PDEs in the so called Cheeger-Gromov topology on the space of complete pointed riemannian manifolds.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47319127","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: 4
E-series of character varieties of non-orientable surfaces 非定向表面的e系列字符品种
IF 0.7 4区 数学
Annales De L Institut Fourier Pub Date : 2020-08-31 DOI: 10.5802/aif.3540
E. Letellier, F. Rodriguez-Villegas
{"title":"E-series of character varieties of non-orientable surfaces","authors":"E. Letellier, F. Rodriguez-Villegas","doi":"10.5802/aif.3540","DOIUrl":"https://doi.org/10.5802/aif.3540","url":null,"abstract":"In this paper we are interested in two kinds of (stacky) character varieties associated to a compact non-orientable surface. (A) We consider the quotient stack of the space of representations of the fundamental group of this surface to GL(n). (B) We choose a set of k-punctures on the surface and a generic k-tuple of semisimple conjugacy classes of GL(n), and we consider the stack of anti-invariant local systems on the orientation cover of the surface with local monodromies around the punctures given by the prescribed conjugacy classes. We compute the number of points of these spaces over finite fields from which we get a formula for their E-series (a certain specialization of the mixed Poincare series). In case (B) we give a conjectural formula for the full mixed Poincare series.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42421423","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: 10
Coronizations and big pieces in metric spaces 加冕仪式和米制空间中的大件
IF 0.7 4区 数学
Annales De L Institut Fourier Pub Date : 2020-08-26 DOI: 10.5802/aif.3518
S. Bortz, J. Hoffman, S. Hofmann, J. García, Kaj Nystrom
{"title":"Coronizations and big pieces in metric spaces","authors":"S. Bortz, J. Hoffman, S. Hofmann, J. García, Kaj Nystrom","doi":"10.5802/aif.3518","DOIUrl":"https://doi.org/10.5802/aif.3518","url":null,"abstract":"We prove that coronizations with respect to arbitrary d-regular sets (not necessarily graphs) imply big pieces squared of these (approximating) sets. This is known (and due to David and Semmes in the case of sufficiently large co-dimension, and to Azzam and Schul in general) in the (classical) setting of Euclidean spaces with Hausdorff measure of integer dimension, where the approximating sets are Lipschitz graphs. Our result is a far reaching generalization of these results and we prove that coronizations imply big pieces squared is a generic property. In particular, our result applies, when suitably interpreted, in metric spaces having a fixed positive (perhaps non-integer) dimension, equipped with a Borel regular measure and with arbitrary approximating sets. As a novel application we highlight how to utilize this general setting in the context of parabolic uniform rectifiability.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46893382","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: 10
Local-to-Global-rigidity of lattices in SL n (𝕂) SLn中格的局部到全局刚度(𝕂)
IF 0.7 4区 数学
Annales De L Institut Fourier Pub Date : 2020-08-17 DOI: 10.5802/aif.3490
Amandine Escalier
{"title":"Local-to-Global-rigidity of lattices in SL n (𝕂)","authors":"Amandine Escalier","doi":"10.5802/aif.3490","DOIUrl":"https://doi.org/10.5802/aif.3490","url":null,"abstract":"A vertex-transitive graph $mathcal{G}$ is called Local-to-Global rigid if there exists $R>0$ such that every other graph whose balls of radius $R$ are isometric to the balls of radius $R$ in $mathcal{G}$ is covered by $mathcal{G}$. An example of such a graph is given by the Bruhat-Tits building of $PSL_n(mathbb{K})$ with $ngeq 4$ and $mathbb{K}$ a non-Archimedean local field of characteristic zero.. In this paper we extend this rigidity property to a class of graphs quasi-isometric to the building including torsion-free lattices of $SL_n(mathbb{K})$. The demonstration is the occasion to prove a result on the local structure of the building. We show that if we fix a $PSL_n(mathbb{K})$-orbit in it, then a vertex is uniquely determined by the neighbouring vertices in this orbit.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41745386","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
Examples of deformed G2-instantons/Donaldson–Thomas connections 变形G2-instantons/ Donaldson-Thomas连接的例子
IF 0.7 4区 数学
Annales De L Institut Fourier Pub Date : 2020-07-22 DOI: 10.5802/aif.3465
Jason D. Lotay, Gonçalo Oliveira
{"title":"Examples of deformed G2-instantons/Donaldson–Thomas connections","authors":"Jason D. Lotay, Gonçalo Oliveira","doi":"10.5802/aif.3465","DOIUrl":"https://doi.org/10.5802/aif.3465","url":null,"abstract":"In this note, we provide the first non-trivial examples of deformed G_2-instantons, originally called deformed Donaldson-Thomas connections. As a consequence, we see how deformed G_2-instantons can be used to distinguish between nearly parallel G_2-structures and isometric G_2-structures on 3-Sasakian 7-manifolds. Our examples give non-trivial deformed G_2-instantons with obstructed deformation theory and situations where the moduli space of deformed G_2-instantons has components of different dimensions. We finally study the relation between our examples and a Chern-Simons type functional which has deformed G_2-instantons as critical points.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48745652","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: 10
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