We study the geodesic flow of a compact surface without conjugate points and genus greater than one and continuous Green bundles. Identifying each strip of bi-asymptotic geodesics induces an equivalence relation on the unit tangent bundle. Its quotient space is shown to carry the structure of a 3-dimensional compact manifold. This manifold carries a canonically defined continuous flow which is expansive, time-preserving semi-conjugate to the geodesic flow, and has a local product structure. An essential step towards the proof of these properties is to study regularity properties of the horospherical foliations and to show that they are indeed tangent to the Green subbundles. As an application it is shown that the geodesic flow has a unique measure of maximal entropy.
{"title":"Geodesic flows modeled by expansive flows: Compact surfaces without conjugate points and continuous Green bundles","authors":"Rafael O. Ruggiero, Katrin Gelfert","doi":"10.5802/aif.3574","DOIUrl":"https://doi.org/10.5802/aif.3574","url":null,"abstract":"We study the geodesic flow of a compact surface without conjugate points and genus greater than one and continuous Green bundles. Identifying each strip of bi-asymptotic geodesics induces an equivalence relation on the unit tangent bundle. Its quotient space is shown to carry the structure of a 3-dimensional compact manifold. This manifold carries a canonically defined continuous flow which is expansive, time-preserving semi-conjugate to the geodesic flow, and has a local product structure. An essential step towards the proof of these properties is to study regularity properties of the horospherical foliations and to show that they are indeed tangent to the Green subbundles. As an application it is shown that the geodesic flow has a unique measure of maximal entropy.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135043897","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}
We give an explicit geometric formula for the twisted orbital integrals using the method of the hypoelliptic Laplacian developed by Bismut. Combining with the twisted trace formula, we can evaluate the equivariant trace of the heat operators of the Laplacians on a compact locally symmetric space. In particular, we revisit the equivariant local index theorems and twisted L 2 -torsions for locally symmetric spaces.
{"title":"Hypoelliptic Laplacian and twisted trace formula","authors":"Bingxiao Liu","doi":"10.5802/aif.3566","DOIUrl":"https://doi.org/10.5802/aif.3566","url":null,"abstract":"We give an explicit geometric formula for the twisted orbital integrals using the method of the hypoelliptic Laplacian developed by Bismut. Combining with the twisted trace formula, we can evaluate the equivariant trace of the heat operators of the Laplacians on a compact locally symmetric space. In particular, we revisit the equivariant local index theorems and twisted L 2 -torsions for locally symmetric spaces.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135043742","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}
We provide a simple method for obtaining new Liouville-type theorems for positive supersolutions of the elliptic problem -Δ p u+b(x)|∇u| pq q+1 =c(x)u q in Ω, where Ω is an exterior domain in ℝ N with N≥p>1 and q≥p-1. In the case q≠p-1, we mainly deal with potentials of the type b(x)=|x| a , c(x)=λ|x| σ , where λ>0 and a,σ∈ℝ. We show that positive supersolutions do not exist in some ranges of the parameters p,q,a,σ, which turn out to be optimal. When q=p-1, we consider the above problem with general weights b(x)≥0, c(x)>0 and we assume that c(x)-b p (x) p p >0 for large |x|, but we also allow the case lim |x|→∞ [c(x)-b p (x) p p ]=0. The weights b and c are allowed to be unbounded. We prove that if this equation has a positive supersolution, then the potentials must satisfy a related differential inequality not depending on the supersolution. We also establish sufficient conditions for the nonexistence of positive supersolutions in relationship with the values of τ:=lim sup |x|→∞ |x|b(x)≤∞. A key ingredient in the proofs is a generalized Hardy-type inequality associated to the p-Laplace operator.
给出了在Ω中求解椭圆型问题-Δ p u+b(x)|∇u| pq q+1 =c(x)u q的新liouvile型定理的一种简单方法，其中Ω是一个N≥p>1且q≥p-1的外域。在q≠p-1的情况下，我们主要处理b(x)=|x| a, c(x)=λ|x| σ的势，其中λ>0，且a，σ∈x。我们证明了在参数p,q,a，σ的某些范围内不存在正超解，这是最优的。当q=p-1时，考虑上述问题具有一般权值b(x)≥0,c(x)>0，并假设c(x)-b p (x) p p >0，对于较大的|x|，我们也允许lim |x|→∞[c(x)-b p (x) p p]=0。b和c的权值是无界的。我们证明了如果这个方程有一个正的超解，那么势必须满足一个不依赖于超解的相关微分不等式。建立了与τ =lim sup |x|→∞|x|b(x)≤∞有关的正超解不存在的充分条件。证明中的一个关键因素是与p-拉普拉斯算子相关的广义hardy型不等式。
{"title":"Positive supersolutions of non-autonomous quasilinear elliptic equations with mixed reaction","authors":"Asadollah Aghajani, Vicenţiu D. Rădulescu","doi":"10.5802/aif.3576","DOIUrl":"https://doi.org/10.5802/aif.3576","url":null,"abstract":"We provide a simple method for obtaining new Liouville-type theorems for positive supersolutions of the elliptic problem -Δ p u+b(x)|∇u| pq q+1 =c(x)u q in Ω, where Ω is an exterior domain in ℝ N with N≥p>1 and q≥p-1. In the case q≠p-1, we mainly deal with potentials of the type b(x)=|x| a , c(x)=λ|x| σ , where λ>0 and a,σ∈ℝ. We show that positive supersolutions do not exist in some ranges of the parameters p,q,a,σ, which turn out to be optimal. When q=p-1, we consider the above problem with general weights b(x)≥0, c(x)>0 and we assume that c(x)-b p (x) p p >0 for large |x|, but we also allow the case lim |x|→∞ [c(x)-b p (x) p p ]=0. The weights b and c are allowed to be unbounded. We prove that if this equation has a positive supersolution, then the potentials must satisfy a related differential inequality not depending on the supersolution. We also establish sufficient conditions for the nonexistence of positive supersolutions in relationship with the values of τ:=lim sup |x|→∞ |x|b(x)≤∞. A key ingredient in the proofs is a generalized Hardy-type inequality associated to the p-Laplace operator.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135043743","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}
In this paper we prove that given a pair (X,D) of a threefold X and a boundary divisor D with mild singularities, if (K X +D) is movable, then the orbifold second Chern class c 2 of (X,D) is pseudoeffective. This generalizes the classical result of Miyaoka on the pseudoeffectivity of c 2 for minimal models. As an application, we give a simple solution to Kawamata’s effective non-vanishing conjecture in dimension 3, where we prove that H 0 (X,K X +H)≠0, whenever K X +H is nef and H is an ample, effective, reduced Cartier divisor. Furthermore, we study Lang–Vojta’s conjecture for codimension one subvarieties and prove that minimal threefolds of general type have only finitely many Fano, Calabi–Yau or Abelian subvarieties of codimension one that are mildly singular and whose numerical classes belong to the movable cone.
本文证明了给定一个三重X对(X,D)和一个温和奇异的边界因子D，如果(K X +D)是可动的，则(X,D)的二阶陈氏类c2是伪有效的。这推广了Miyaoka关于最小模型下c2伪有效性的经典结果。作为应用，我们给出了3维Kawamata有效不消失猜想的一个简单解，证明了当K X +H为nef且H是一个充分有效的约简Cartier除数时，H 0 (X,K X +H)≠0。进一步研究了Lang-Vojta关于余维数1子变种的猜想，证明了一般型极小三折只有有限多个余维数1的Fano、Calabi-Yau或Abelian子变种是微奇异的，其数值类属于可动锥。
{"title":"Orbifold Chern classes inequalities and applications","authors":"Erwan Rousseau, Behrouz Taji","doi":"10.5802/aif.3571","DOIUrl":"https://doi.org/10.5802/aif.3571","url":null,"abstract":"In this paper we prove that given a pair (X,D) of a threefold X and a boundary divisor D with mild singularities, if (K X +D) is movable, then the orbifold second Chern class c 2 of (X,D) is pseudoeffective. This generalizes the classical result of Miyaoka on the pseudoeffectivity of c 2 for minimal models. As an application, we give a simple solution to Kawamata’s effective non-vanishing conjecture in dimension 3, where we prove that H 0 (X,K X +H)≠0, whenever K X +H is nef and H is an ample, effective, reduced Cartier divisor. Furthermore, we study Lang–Vojta’s conjecture for codimension one subvarieties and prove that minimal threefolds of general type have only finitely many Fano, Calabi–Yau or Abelian subvarieties of codimension one that are mildly singular and whose numerical classes belong to the movable cone.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135043879","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}
{"title":"Lifting Semistability in Finitely Generated Ascending HNN-Extensions","authors":"F. F. Lasheras, M. Mihalik","doi":"10.5802/aif.3599","DOIUrl":"https://doi.org/10.5802/aif.3599","url":null,"abstract":"","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42193274","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}
Ryan Blair, P. Cahn, Alexandra Kjuchukova, J. Meier
{"title":"Note on three-fold branched covers of S 4 ","authors":"Ryan Blair, P. Cahn, Alexandra Kjuchukova, J. Meier","doi":"10.5802/aif.3588","DOIUrl":"https://doi.org/10.5802/aif.3588","url":null,"abstract":"","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45519452","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}
{"title":"On the Iwasawa μ-invariant and λ-invariant associated to tensor products of newforms","authors":"D. Delbourgo","doi":"10.5802/aif.3593","DOIUrl":"https://doi.org/10.5802/aif.3593","url":null,"abstract":"","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47539427","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}
— The article studies the nonlinear Stokes phenomenon at the irregular singularity of the Fifth Painlevé equation from the point of view of confluence from the Sixth Painlevé equation. This approach is developed separately on both sides of the Riemann–Hilbert correspondence. On the side of the Painlevé–Okamoto foliation, the relation between the nonlinear monodromy group of Painlevé VI and the “nonlinear wild monodromy pseudogroup” of Painlevé V (the pseudogroup generated by nonlinear Stokes operators and nonlinear exponential torus) is explained. On the side of the associated linear isomonodromic problems, the “wild” character variety (the space of the linear monodromy and Stokes data) of Painlevé V is constructed through a birational transformation from the one of Painlevé VI. Explicit formulas for the action of the “nonlinear wild monodromy” of Painlevé V on its character variety are then obtained by transporting the description of the action of the nonlinear monodromy of Painlevé VI on its character variety to that of Painlevé V. Résumé. — L’article étudie le phénomène de Stokes non linéaire à la singularité irrégulière de la Cinquième équation de Painlevé du point de vue de la confluence à partir de la Sixième équation de Painlevé. Cette approche est développée séparément des deux côtés de la correspondance de Riemann–Hilbert. Du côté du feuilletage de Painlevé–Okamoto, la relation entre le groupe de monodromie nonlinéaire de Painlevé VI et le « pseudogroupe de monodromie sauvage non-linéaire » de Painlevé V (le pseudogroupe engendré par les opérateurs de Stokes non-linéaires et le tore exponentiel non-linéaire) est expliquée. Du côté des problèmes isomonodromiques linéaires associés, la variété de caractères « sauvages » (l’espace de la monodromie linéaire et des données de Stokes) de Painlevé V est construite par une transformation birationnelle à partir de celle de Painlevé VI. On obtient alors des formules explicites de l’action de la « monodromie sauvage non-linéaire » de Painlevé V sur sa variété de caractères en transportant la description de l’action de la monodromie non-linéaire de Painlevé VI sur sa variété de caractères à celle de Painlevé V.
{"title":"Wild monodromy of the Fifth Painlevé equation and its action on wild character variety: an approach of confluence","authors":"Martin Klimeš","doi":"10.5802/aif.3579","DOIUrl":"https://doi.org/10.5802/aif.3579","url":null,"abstract":"— The article studies the nonlinear Stokes phenomenon at the irregular singularity of the Fifth Painlevé equation from the point of view of confluence from the Sixth Painlevé equation. This approach is developed separately on both sides of the Riemann–Hilbert correspondence. On the side of the Painlevé–Okamoto foliation, the relation between the nonlinear monodromy group of Painlevé VI and the “nonlinear wild monodromy pseudogroup” of Painlevé V (the pseudogroup generated by nonlinear Stokes operators and nonlinear exponential torus) is explained. On the side of the associated linear isomonodromic problems, the “wild” character variety (the space of the linear monodromy and Stokes data) of Painlevé V is constructed through a birational transformation from the one of Painlevé VI. Explicit formulas for the action of the “nonlinear wild monodromy” of Painlevé V on its character variety are then obtained by transporting the description of the action of the nonlinear monodromy of Painlevé VI on its character variety to that of Painlevé V. Résumé. — L’article étudie le phénomène de Stokes non linéaire à la singularité irrégulière de la Cinquième équation de Painlevé du point de vue de la confluence à partir de la Sixième équation de Painlevé. Cette approche est développée séparément des deux côtés de la correspondance de Riemann–Hilbert. Du côté du feuilletage de Painlevé–Okamoto, la relation entre le groupe de monodromie nonlinéaire de Painlevé VI et le « pseudogroupe de monodromie sauvage non-linéaire » de Painlevé V (le pseudogroupe engendré par les opérateurs de Stokes non-linéaires et le tore exponentiel non-linéaire) est expliquée. Du côté des problèmes isomonodromiques linéaires associés, la variété de caractères « sauvages » (l’espace de la monodromie linéaire et des données de Stokes) de Painlevé V est construite par une transformation birationnelle à partir de celle de Painlevé VI. On obtient alors des formules explicites de l’action de la « monodromie sauvage non-linéaire » de Painlevé V sur sa variété de caractères en transportant la description de l’action de la monodromie non-linéaire de Painlevé VI sur sa variété de caractères à celle de Painlevé V.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49532728","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}
{"title":"Décomposition en blocs de la catégorie des représentations ℓ-modulaires lisses de longueur finie de GL","authors":"Bastien Drevon, V. Sécherre","doi":"10.5802/aif.3572","DOIUrl":"https://doi.org/10.5802/aif.3572","url":null,"abstract":"","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49448877","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}
{"title":"Circumcenter extension of Moebius maps to CAT(-1) spaces","authors":"Kingshook Biswas","doi":"10.5802/aif.3582","DOIUrl":"https://doi.org/10.5802/aif.3582","url":null,"abstract":"","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47787050","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}
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