Pub Date : 2013-01-01DOI: 10.2422/2036-2145.201107_006
G. Alberti, S. Bianchini, Gianluca Crippa
We consider certain properties of maps of class C 2 from R d to R d 1 that are strictly related to Sard's theorem, and show that some of them can be extended to Lipschitz maps, while others still require some additional regularity. We also give examples showing that, in term of regularity, our results are optimal.
{"title":"Structure of level sets and Sard-type properties of Lipschitz maps","authors":"G. Alberti, S. Bianchini, Gianluca Crippa","doi":"10.2422/2036-2145.201107_006","DOIUrl":"https://doi.org/10.2422/2036-2145.201107_006","url":null,"abstract":"We consider certain properties of maps of class C 2 from R d to R d 1 that are strictly related to Sard's theorem, and show that some of them can be extended to Lipschitz maps, while others still require some additional regularity. We also give examples showing that, in term of regularity, our results are optimal.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"26 1","pages":"863-902"},"PeriodicalIF":1.4,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75831107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-01-01DOI: 10.2422/2036-2145.201010_011
M. Pino, M. Musso, F. Pacard, A. Pistoia
— We construct sequences of sign changing solutions for some conformally invariant semilinear elliptic equation which is defined in Sn, when n ≥ 4. The solutions we obtain have large energy and concentrate along some special submanifolds of Sn. For example, when n ≥ 4, we obtain sequences of solutions whose energy concentrates along one great circle or finitely many great circles which are linked (they correspond to Hopf links embedded in S3 × {0} ⊂ Sn). In dimension n ≥ 5, we obtain sequences of solutions whose energy concentrates along a two dimensional torus (which corresponds to a Clifford torus embedded in S3 × {0} ⊂ Sn).
{"title":"Torus action on S^n and sign changing solutions for conformally invariant equations","authors":"M. Pino, M. Musso, F. Pacard, A. Pistoia","doi":"10.2422/2036-2145.201010_011","DOIUrl":"https://doi.org/10.2422/2036-2145.201010_011","url":null,"abstract":"— We construct sequences of sign changing solutions for some conformally invariant semilinear elliptic equation which is defined in Sn, when n ≥ 4. The solutions we obtain have large energy and concentrate along some special submanifolds of Sn. For example, when n ≥ 4, we obtain sequences of solutions whose energy concentrates along one great circle or finitely many great circles which are linked (they correspond to Hopf links embedded in S3 × {0} ⊂ Sn). In dimension n ≥ 5, we obtain sequences of solutions whose energy concentrates along a two dimensional torus (which corresponds to a Clifford torus embedded in S3 × {0} ⊂ Sn).","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"2 1","pages":"209-237"},"PeriodicalIF":1.4,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81526229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-01-01DOI: 10.2422/2036-2145.201103_005
C. Cinti, K. Nyström, S. Polidoro
We prove a Carleson type estimate, in Lipschitz type domains, for non-negative solutions to a class of second order degenerate differential operators of Kolmogorov type of the form L = Sigma(m)(i,j ...
{"title":"A Carleson-type estimate in Lipschitz type domains for non-negative solutions to Kolmogorov operators","authors":"C. Cinti, K. Nyström, S. Polidoro","doi":"10.2422/2036-2145.201103_005","DOIUrl":"https://doi.org/10.2422/2036-2145.201103_005","url":null,"abstract":"We prove a Carleson type estimate, in Lipschitz type domains, for non-negative solutions to a class of second order degenerate differential operators of Kolmogorov type of the form L = Sigma(m)(i,j ...","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"34 1","pages":"439-465"},"PeriodicalIF":1.4,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82696908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-07-03DOI: 10.2422/2036-2145.201007_002
Z. Jiang
We give a complete description of all smooth projective complex varieties with q(X) = dim(X) and P2(X) = 2.
给出了q(X) = dim(X)且P2(X) = 2的所有光滑射影复变的完整描述。
{"title":"Varieties with $q(X)=dim(X)$ and $P_2(X)=2$","authors":"Z. Jiang","doi":"10.2422/2036-2145.201007_002","DOIUrl":"https://doi.org/10.2422/2036-2145.201007_002","url":null,"abstract":"We give a complete description of all smooth projective complex \u0000varieties with q(X) = dim(X) and P2(X) = 2.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"13 1","pages":"243-258"},"PeriodicalIF":1.4,"publicationDate":"2012-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88449003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-06-13DOI: 10.2422/2036-2145.201304_001
A. Bandini, M. Valentino
Let F be a global function field of characteristic p > 0, K/F an l-adic Lie extension unramified outside a finite set of places S and A/F an abelian variety. We study SelA(K) ∨ (the Pontrjagin dual of the Selmer group) and (under some mild hypotheses) prove that it is a finitely generated Zl((Gal(K/F)))-module via generalizations of Mazur's Control Theorem. If Gal(K/F) has no elements of order l and contains a closed normal subgroup H such that Gal(K/F)/H ≃ Zl, we are able to give sufficient conditions forSelA(K) ∨ to be finitely generated as Zl((H))-module and, consequently, a torsion Zl((Gal(K/F)))-module. We deal with both cases l 6 p and l = p.
{"title":"Control theorems for l-adic Lie extensions of global function fields","authors":"A. Bandini, M. Valentino","doi":"10.2422/2036-2145.201304_001","DOIUrl":"https://doi.org/10.2422/2036-2145.201304_001","url":null,"abstract":"Let F be a global function field of characteristic p > 0, K/F an l-adic Lie extension unramified outside a finite set of places S and A/F an abelian variety. We study SelA(K) ∨ (the Pontrjagin dual of the Selmer group) and (under some mild hypotheses) prove that it is a finitely generated Zl((Gal(K/F)))-module via generalizations of Mazur's Control Theorem. If Gal(K/F) has no elements of order l and contains a closed normal subgroup H such that Gal(K/F)/H ≃ Zl, we are able to give sufficient conditions forSelA(K) ∨ to be finitely generated as Zl((H))-module and, consequently, a torsion Zl((Gal(K/F)))-module. We deal with both cases l 6 p and l = p.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"26 1","pages":"1065-1092"},"PeriodicalIF":1.4,"publicationDate":"2012-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90581875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-16DOI: 10.2422/2036-2145.201302_002
Lukas Pottmeyer
Let E be an elliptic curve defined over a number field K with fixed non-archimedean absolute value v of split-multiplicative reduction, and let f be an associated Lattes map. Baker proved in [3] that the Neron-Tate height on E is either zero or bounded from below by a positive constant, for all points of bounded ramification over v. In this paper we make this bound effective and prove an analogue result for the canonical height associated to f. We also study variations of this result by changing the reduction type of E at v. This will lead to examples of fields F such that the Neron-Tate height on non-torsion points in E (F) is bounded from below by a positive constant and the height associated to f gets arbitrarily small on F.
设E是定义在数域K上的一条椭圆曲线，具有分裂乘化的固定非阿基米德绝对值v，设f是一个关联的拿铁映射。Baker在[3]中证明了E上的Neron-Tate高度要么为零，要么从下面有一个正常数，所有点的有界衍生物在诉在本文中,我们把这个绑定有效和证明标准的模拟结果高度相关f。我们也研究变异的结果通过改变类型的E v .这将导致减少域f的例子,这样Neron-Tate高度在E non-torsion点(f)是由积极的常数和有界从下面相关的高度被任意小f。
{"title":"Heights of points with bounded ramification","authors":"Lukas Pottmeyer","doi":"10.2422/2036-2145.201302_002","DOIUrl":"https://doi.org/10.2422/2036-2145.201302_002","url":null,"abstract":"Let E be an elliptic curve defined over a number field K with fixed non-archimedean absolute value v of split-multiplicative reduction, and let f be an associated Lattes map. Baker proved in [3] that the Neron-Tate height on E is either zero or bounded from below by a positive constant, for all points of bounded ramification over v. In this paper we make this bound effective and prove an analogue result for the canonical height associated to f. We also study variations of this result by changing the reduction type of E at v. This will lead to examples of fields F such that the Neron-Tate height on non-torsion points in E (F) is bounded from below by a positive constant and the height associated to f gets arbitrarily small on F.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"28 1","pages":"965-981"},"PeriodicalIF":1.4,"publicationDate":"2012-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78202125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-01-01DOI: 10.2422/2036-2145.201003_009
T. Leistner, P. Nurowski
We present conformal structures in signature (3, 2) for which the holonomy of the Fefferman-Graham ambient metric is equal to the non-compact exceptional Lie group G2(2). We write down the resulting 8-parameter family of G2(2)-metrics in dimension seven explicitly in an appropriately chosen coordinate system on the ambient space.
{"title":"Ambient metrics with exceptional holonomy","authors":"T. Leistner, P. Nurowski","doi":"10.2422/2036-2145.201003_009","DOIUrl":"https://doi.org/10.2422/2036-2145.201003_009","url":null,"abstract":"We present conformal structures in signature (3, 2) for which the holonomy of the Fefferman-Graham ambient metric is equal to the non-compact exceptional Lie group G2(2). We write down the resulting 8-parameter family of G2(2)-metrics in dimension seven explicitly in an appropriately chosen coordinate system on the ambient space.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"4 1","pages":"407-436"},"PeriodicalIF":1.4,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73888390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-08-05DOI: 10.2422/2036-2145.201403_004
B. Kleiner, J. Mackay
This is an exposition of the theory of differentiable structures onmetric measure spaces, in the sense of Cheeger and Keith
这是在Cheeger和Keith的意义上，对对称测度空间的可微结构理论的阐述
{"title":"DIFFERENTIABLE STRUCTURES ON METRIC MEASURE SPACES: A PRIMER","authors":"B. Kleiner, J. Mackay","doi":"10.2422/2036-2145.201403_004","DOIUrl":"https://doi.org/10.2422/2036-2145.201403_004","url":null,"abstract":"This is an exposition of the theory of differentiable structures onmetric \u0000measure spaces, in the sense of Cheeger and Keith","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"66 1","pages":"41-64"},"PeriodicalIF":1.4,"publicationDate":"2011-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80367090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-03-10DOI: 10.2422/2036-2145.201205_010
L. David, I. Strachan
We construct a duality for F-manifolds with eventual identities and certain special families of connections and we study its interactions with several well-known constructions from the theory of Frobenius and F-manifolds.
{"title":"Symmetries of F-manifolds with eventual identities and special families of connections","authors":"L. David, I. Strachan","doi":"10.2422/2036-2145.201205_010","DOIUrl":"https://doi.org/10.2422/2036-2145.201205_010","url":null,"abstract":"We construct a duality for F-manifolds with eventual identities and certain special families of connections and we study its interactions with several well-known constructions from the theory of Frobenius and F-manifolds.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"26 1","pages":"641-674"},"PeriodicalIF":1.4,"publicationDate":"2011-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86474663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-03-01DOI: 10.2422/2036-2145.201107_005
Attila B'erczes, J. Evertse, K'alm'an GyHory
Let A = Z(x1;:::;xr) Z be a domain which is nitely gen- erated over Z and integrally closed in its quotient eld L. Further, let K be a nite extension eld of L. An A-order in K is a domainO A with quotient eld K which is integral overA. A-orders inK of the typeA( ) are called monogenic. It was proved by Gy} ory (10) that for any given A-order O in K there are at most nitely many A-equivalence classes of 2 O with A( ) = O, where two elements ; of O are called A-equivalent if = u +a for some u2 A , a2 A. If the number of A-equivalence classes of with A( ) =O is at least k, we callO k times monogenic. In this paper we study orders which are more than one time monogenic.
{"title":"MULTIPLY MONOGENIC ORDERS","authors":"Attila B'erczes, J. Evertse, K'alm'an GyHory","doi":"10.2422/2036-2145.201107_005","DOIUrl":"https://doi.org/10.2422/2036-2145.201107_005","url":null,"abstract":"Let A = Z(x1;:::;xr) Z be a domain which is nitely gen- erated over Z and integrally closed in its quotient eld L. Further, let K be a nite extension eld of L. An A-order in K is a domainO A with quotient eld K which is integral overA. A-orders inK of the typeA( ) are called monogenic. It was proved by Gy} ory (10) that for any given A-order O in K there are at most nitely many A-equivalence classes of 2 O with A( ) = O, where two elements ; of O are called A-equivalent if = u +a for some u2 A , a2 A. If the number of A-equivalence classes of with A( ) =O is at least k, we callO k times monogenic. In this paper we study orders which are more than one time monogenic.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"2 1","pages":"467-497"},"PeriodicalIF":1.4,"publicationDate":"2011-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84538716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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