We prove that, for almost all irrational ρ ∈ (0, 1), every two C2+α-smooth, α ∈ (0, 1), circle diffeomorphisms with a break point, i.e., a singular point where the derivative has a jump discontinuity, with the same rotation number ρ and the same size of the break c ∈ R+{1}, are C1-smoothly conjugate to each other. Résumé Nous démontrons que pour presque tous les irrationnels ρ ∈ (0, 1), deux difféomorphismes du cercle C2+α lisses, α ∈ (0, 1), avec un point de singularité de type rupture où la dérivée a une discontinuité de saut, avec le même nombre de rotation ρ et la même taille de rupture c ∈ R+{1}, sont C1-conjugués l’un à l’autre. 2000 Mathematics Subject Classification: 37E10, 37E20.
We骄傲,从for all的非理性繁荣ρ∈(0,1),les deux C2 +α,α-smooth∈(0,1),circle diffeomorphisms with a break point,即,a点或者是一种独特的衍生物has a jump the discontinuity,编号ρand the same with the same轮换尺寸of the旅行车c∈R + {1}, are to C1-smoothly共轭物的朋友。才总结出我们对于几乎所有非理性ρ∈(0,1),两个光滑的圆的difféomorphismes C2 +α,α∈(0,1),与一个奇点断裂,那里有派生型与相同数量的旋转跳跃不连续点,ρ和断裂同样大小的c∈R + {1},则C1-conjugués彼此。2000数学科目分类:37E10, 37E20。
{"title":"C^1-rigidity of circle maps with breaks for almost all rotation numbers","authors":"K. Khanin, S. Kocić, E. Mazzeo","doi":"10.24033/ASENS.2342","DOIUrl":"https://doi.org/10.24033/ASENS.2342","url":null,"abstract":"We prove that, for almost all irrational ρ ∈ (0, 1), every two C2+α-smooth, α ∈ (0, 1), circle diffeomorphisms with a break point, i.e., a singular point where the derivative has a jump discontinuity, with the same rotation number ρ and the same size of the break c ∈ R+{1}, are C1-smoothly conjugate to each other. Résumé Nous démontrons que pour presque tous les irrationnels ρ ∈ (0, 1), deux difféomorphismes du cercle C2+α lisses, α ∈ (0, 1), avec un point de singularité de type rupture où la dérivée a une discontinuité de saut, avec le même nombre de rotation ρ et la même taille de rupture c ∈ R+{1}, sont C1-conjugués l’un à l’autre. 2000 Mathematics Subject Classification: 37E10, 37E20.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"7 1","pages":"1163-1203"},"PeriodicalIF":1.9,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79006444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We reconstruct compactly supported potentials with only half a derivative in L from the scattering amplitude at a fixed energy. For this we draw a connection between the recently introduced method of Bukhgeim, which uniquely determined the potential from the Dirichletto-Neumann map, and a question of Carleson regarding the convergence to initial data of solutions to time-dependent Schrödinger equations. We also provide examples of compactly supported potentials, with s derivatives in L for any s < 1/2, which cannot be recovered by these means. Thus the recovery method has a different threshold in terms of regularity than the corresponding uniqueness result.
{"title":"Unbounded potential recovery in the plane","authors":"K. Astala, D. Faraco, K. Rogers","doi":"10.24033/ASENS.2302","DOIUrl":"https://doi.org/10.24033/ASENS.2302","url":null,"abstract":"We reconstruct compactly supported potentials with only half a derivative in L from the scattering amplitude at a fixed energy. For this we draw a connection between the recently introduced method of Bukhgeim, which uniquely determined the potential from the Dirichletto-Neumann map, and a question of Carleson regarding the convergence to initial data of solutions to time-dependent Schrödinger equations. We also provide examples of compactly supported potentials, with s derivatives in L for any s < 1/2, which cannot be recovered by these means. Thus the recovery method has a different threshold in terms of regularity than the corresponding uniqueness result.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"82 1","pages":"1027-1051"},"PeriodicalIF":1.9,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83259757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove a combinatorial criterion for K-stability of a Q-Fano spherical variety with respect to equivariant special test configurations, in terms of its moment polytope and some combinatorial data associated to the open orbit. Combined with the equivariant version of the Yau-Tian-Donaldson conjecture for Fano manifolds proved by Datar and Szekelyhidi, it yields a criterion for the existence of a Kahler-Einstein metric on a spherical Fano manifold. The results hold also for modified K-stability and existence of Kahler-Ricci solitons.
{"title":"K-stability of Fano spherical varieties","authors":"Thibaut Delcroix","doi":"10.24033/ASENS.2430","DOIUrl":"https://doi.org/10.24033/ASENS.2430","url":null,"abstract":"We prove a combinatorial criterion for K-stability of a Q-Fano spherical variety with respect to equivariant special test configurations, in terms of its moment polytope and some combinatorial data associated to the open orbit. Combined with the equivariant version of the Yau-Tian-Donaldson conjecture for Fano manifolds proved by Datar and Szekelyhidi, it yields a criterion for the existence of a Kahler-Einstein metric on a spherical Fano manifold. The results hold also for modified K-stability and existence of Kahler-Ricci solitons.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"36 1","pages":"615-662"},"PeriodicalIF":1.9,"publicationDate":"2016-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84841931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove that the local etale fundamental group of a strongly $F$-regular singularity is finite (and likewise for the etale fundamental group of the complement of a codimension $geq 2$ set), analogous to results of Xu and Greb-Kebekus-Peternell for KLT singularities in characteristic zero. In fact our result is effective, we show that the reciprocal of the $F$-signature of the singularity gives a bound on the size of this fundamental group. To prove these results and their corollaries, we develop new transformation rules for the $F$-signature under finite etale-in-codimension-one extensions. As another consequence of these transformation rules, we also obtain purity of the branch locus over rings with mild singularities (particularly if the $F$-signature is $> 1/2$). Finally, we generalize our $F$-signature transformation rules to the context of pairs and not-necessarily etale-in-codimension-one extensions, obtaining an analog of another result of Xu.
{"title":"Fundamental groups of F-regular singularities via F-signature","authors":"Javier Carvajal-Rojas, Karl Schwede, Kevin Tucker","doi":"10.24033/asens.2370","DOIUrl":"https://doi.org/10.24033/asens.2370","url":null,"abstract":"We prove that the local etale fundamental group of a strongly $F$-regular singularity is finite (and likewise for the etale fundamental group of the complement of a codimension $geq 2$ set), analogous to results of Xu and Greb-Kebekus-Peternell for KLT singularities in characteristic zero. In fact our result is effective, we show that the reciprocal of the $F$-signature of the singularity gives a bound on the size of this fundamental group. To prove these results and their corollaries, we develop new transformation rules for the $F$-signature under finite etale-in-codimension-one extensions. As another consequence of these transformation rules, we also obtain purity of the branch locus over rings with mild singularities (particularly if the $F$-signature is $> 1/2$). Finally, we generalize our $F$-signature transformation rules to the context of pairs and not-necessarily etale-in-codimension-one extensions, obtaining an analog of another result of Xu.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"36 1","pages":"993-1016"},"PeriodicalIF":1.9,"publicationDate":"2016-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73523466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Constructible complexes have the same characteristic cycle if they have the same wild ramification, even if the characteristics of the coefficients fields are different.
如果可构复合体具有相同的野分枝，则它们具有相同的特征循环，即使系数场的特征不同。
{"title":"Wild ramification determines the characteristic cycle","authors":"Takeshi Saito, Yuri Yatagawa","doi":"10.24033/asens.2339","DOIUrl":"https://doi.org/10.24033/asens.2339","url":null,"abstract":"Constructible complexes have the same characteristic cycle if they have the same wild ramification, even if the characteristics of the coefficients fields are different.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"11 1","pages":"1065-1079"},"PeriodicalIF":1.9,"publicationDate":"2016-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75150791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper establishes existence of Lipschitz stratifications in the sense of Mostowski for sets which are definable in a polynomially bounded o-minimal structure. We also improve L. van den Dries and P. Speissegger’s preparation theorem for definable functions.
本文建立了在多项式有界o最小结构上可定义的集合在Mostowski意义上的Lipschitz分层的存在性。改进了L. van den Dries和P. Speissegger关于可定义函数的准备定理。
{"title":"Lipschitz stratifications in o-minimal structures","authors":"Nhan Nguyen, G. Valette","doi":"10.24033/ASENS.2286","DOIUrl":"https://doi.org/10.24033/ASENS.2286","url":null,"abstract":"This paper establishes existence of Lipschitz stratifications in the sense of Mostowski for sets which are definable in a polynomially bounded o-minimal structure. We also improve L. van den Dries and P. Speissegger’s preparation theorem for definable functions.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"218 1","pages":"399-421"},"PeriodicalIF":1.9,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77693955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The obstacle problem for the total variation flow","authors":"V. Bögelein, F. Duzaar, Christoph Scheven","doi":"10.24033/ASENS.2306","DOIUrl":"https://doi.org/10.24033/ASENS.2306","url":null,"abstract":"","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"8 1","pages":"1143-1188"},"PeriodicalIF":1.9,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86997880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Resume. The effective version of Chebotarev’s density theorem under the Generalized Riemann Hypothesis and the Artin conjecture (cf. Iwaniec and Kowalski’s Analytic Number Theory, §5.13) involves a numerical invariant of a subset D of a finite group G that we call the Littlewood Complexity of D. We study this invariant in detail. Using this study, and an application of the large sieve, we give improved versions of two standard problems related to Chebotarev : the bound on the first prime in a Frobenian set, and the asymptotics of the set of primes with given Frobenius in an infinite family of Galois extensions. We then give concrete applications to the problem of the factorization of an integral polynomial modulo primes, to the Lang-Trotter conjecture for abelian surfaces, and to the conjecture of Koblitz, with in all three cases better bounds that previously known.
{"title":"Théorème de Chebotarev et complexité de Littlewood","authors":"J. Bellaïche","doi":"10.24033/ASENS.2291","DOIUrl":"https://doi.org/10.24033/ASENS.2291","url":null,"abstract":"Resume. The effective version of Chebotarev’s density theorem under the Generalized Riemann Hypothesis and the Artin conjecture (cf. Iwaniec and Kowalski’s Analytic Number Theory, §5.13) involves a numerical invariant of a subset D of a finite group G that we call the Littlewood Complexity of D. We study this invariant in detail. Using this study, and an application of the large sieve, we give improved versions of two standard problems related to Chebotarev : the bound on the first prime in a Frobenian set, and the asymptotics of the set of primes with given Frobenius in an infinite family of Galois extensions. We then give concrete applications to the problem of the factorization of an integral polynomial modulo primes, to the Lang-Trotter conjecture for abelian surfaces, and to the conjecture of Koblitz, with in all three cases better bounds that previously known.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"21 1","pages":"579-632"},"PeriodicalIF":1.9,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76284806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sur la préservation de la surconvergence par l'image directe d'un morphisme propre et lisse","authors":"Daniel Caro","doi":"10.24033/ASENS.2240","DOIUrl":"https://doi.org/10.24033/ASENS.2240","url":null,"abstract":"","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"76 1","pages":"131-169"},"PeriodicalIF":1.9,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84036238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper studies the behavior of harmonic measured foliations on compact Riemann surfaces. Cascades in the dynamics of such a foliation can occur as its relative periods are varied. We show that in the case of genus 2, the bifurcation locus arising from such a variation is a closed, countable set of R that embeds in ω. Resume Nous etudions le comportement des feuilletages mesures harmoniques sur les surfaces de Riemann compactes. Quands les periodes relatives varient, on peut observer des cascades dans la dynamique d’un tel feuilletage. Dans le cas du genre 2, on montre que le lieu de bifurcation resultant d’une telle variation est un sous-ensemble denombrable et ferme de R, qui se plonge dans ω.
研究了紧致黎曼曲面上谐波测量叶理的行为。在这种叶理作用的动力学中，随着相对周期的变化，会发生级联。我们证明了在属2的情况下，由这种变异引起的分岔轨迹是嵌入在ω中的一个封闭的、可数的R集合。在黎曼紧致曲面上的谐波测量的一致性。量子数周期相对变化，但观察者的级联性和动力学不一致。Dans le cas du genre 2，在montre que le lieu de分叉上产生的d 'une tellle变异是sous-ensemble可命名为et ferme de R, quise plonge Dans ω。
{"title":"Cascades in the Dynamics of Measured Foliations","authors":"C. McMullen","doi":"10.24033/ASENS.2237","DOIUrl":"https://doi.org/10.24033/ASENS.2237","url":null,"abstract":"This paper studies the behavior of harmonic measured foliations on compact Riemann surfaces. Cascades in the dynamics of such a foliation can occur as its relative periods are varied. We show that in the case of genus 2, the bifurcation locus arising from such a variation is a closed, countable set of R that embeds in ω. Resume Nous etudions le comportement des feuilletages mesures harmoniques sur les surfaces de Riemann compactes. Quands les periodes relatives varient, on peut observer des cascades dans la dynamique d’un tel feuilletage. Dans le cas du genre 2, on montre que le lieu de bifurcation resultant d’une telle variation est un sous-ensemble denombrable et ferme de R, qui se plonge dans ω.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"28 1","pages":"1-39"},"PeriodicalIF":1.9,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78002155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：