Pub Date : 2022-12-05DOI: 10.2422/2036-2145.202301_010
F. Polizzi, X. Roulleau
Let $X$ be a compact, complex surface of general type whose cotangent bundle $Omega_X$ is strongly semi-ample. We study the pluri-cotangent maps of $X$, namely the morphisms $psi_n colon mathbb{P}(Omega_X) to mathbb{P}(H^0(X, , S^n Omega_X))$ defined by the vector space of global sections $H^0(X, , S^n Omega_X)$.
{"title":"Pluri-cotangent maps of surfaces of general type","authors":"F. Polizzi, X. Roulleau","doi":"10.2422/2036-2145.202301_010","DOIUrl":"https://doi.org/10.2422/2036-2145.202301_010","url":null,"abstract":"Let $X$ be a compact, complex surface of general type whose cotangent bundle $Omega_X$ is strongly semi-ample. We study the pluri-cotangent maps of $X$, namely the morphisms $psi_n colon mathbb{P}(Omega_X) to mathbb{P}(H^0(X, , S^n Omega_X))$ defined by the vector space of global sections $H^0(X, , S^n Omega_X)$.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78364161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-20DOI: 10.2422/2036-2145.202202_001
F. Albiac, J. L. Ansorena
. Tsirelson’s space T made its appearance in Banach space theory in 1974 soon to become one of the most significant counterexamples in the theory. Its structure broke the ideal pattern that analysts had conceived for a generic Banach space, thus giving rise to the era of pathological examples. Since then, many authors have contributed to the study of different aspects of this special space with an eye on better understanding its idiosyn-crasies. In this paper we are concerned with the greedy-type basis structure of T , a subject that had not been previously explored in the literature. More specifically, we show that Tsirelson’s space and its convexifications T ( p ) for 0 < p < ∞ have uncountably many non-equivalent greedy bases. We also investigate the conditional basis structure of spaces T ( p ) in the range of 0 < p < ∞ and prove that they have uncountably many non-equivalent conditional almost greedy bases.
． 1974年，Tsirelson的空间T出现在Banach空间理论中，并很快成为该理论中最重要的反例之一。它的结构打破了分析师对一般巴拿赫空间的理想模式，从而引发了病态例子的时代。从那时起，许多作者对这个特殊空间的不同方面进行了研究，以期更好地理解它的特质。在本文中，我们关注的是T的贪婪型基结构，这是一个以前没有在文献中探讨过的主题。更具体地说，我们证明了Tsirelson空间及其凸化T (p)对于0 < p <∞具有无数个非等价贪婪基。研究了空间T (p)在0 < p <∞范围内的条件基结构，证明了它们有无数个非等价的条件几乎贪婪基。
{"title":"The structure of greedy-type bases in Tsirelson's space and its convexifications","authors":"F. Albiac, J. L. Ansorena","doi":"10.2422/2036-2145.202202_001","DOIUrl":"https://doi.org/10.2422/2036-2145.202202_001","url":null,"abstract":". Tsirelson’s space T made its appearance in Banach space theory in 1974 soon to become one of the most significant counterexamples in the theory. Its structure broke the ideal pattern that analysts had conceived for a generic Banach space, thus giving rise to the era of pathological examples. Since then, many authors have contributed to the study of different aspects of this special space with an eye on better understanding its idiosyn-crasies. In this paper we are concerned with the greedy-type basis structure of T , a subject that had not been previously explored in the literature. More specifically, we show that Tsirelson’s space and its convexifications T ( p ) for 0 < p < ∞ have uncountably many non-equivalent greedy bases. We also investigate the conditional basis structure of spaces T ( p ) in the range of 0 < p < ∞ and prove that they have uncountably many non-equivalent conditional almost greedy bases.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83972239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-27DOI: 10.2422/2036-2145.202211_003
Javier Pliego
We analyse a collection of mixed moments of the Riemann zeta function and establish the validity of asymptotic formulae. Such examinations are performed both unconditionally and under the assumption of a weaker version of the $abc$ conjecture.
{"title":"Mixed moments of the Riemann zeta function","authors":"Javier Pliego","doi":"10.2422/2036-2145.202211_003","DOIUrl":"https://doi.org/10.2422/2036-2145.202211_003","url":null,"abstract":"We analyse a collection of mixed moments of the Riemann zeta function and establish the validity of asymptotic formulae. Such examinations are performed both unconditionally and under the assumption of a weaker version of the $abc$ conjecture.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84542274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-03DOI: 10.2422/2036-2145.202111_004
V. Grandjean
{"title":"Multplicities and degree relative to a set","authors":"V. Grandjean","doi":"10.2422/2036-2145.202111_004","DOIUrl":"https://doi.org/10.2422/2036-2145.202111_004","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"77 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85914628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-16DOI: 10.2422/2036-2145.202209_012
X. Lamy, E. Marconi
We consider line-energy models of Ginzburg-Landau type in a two-dimensional simply-connected bounded domain. Configurations of vanishing energy have been characterized by Jabin, Otto and Perthame: the domain must be a disk, and the configuration a vortex. We prove a quantitative version of this statement in the class of $C^{1,1}$ domains, improving on previous results by Lorent. In particular, the deviation of the domain from a disk is controlled by a power of the energy, and that power is optimal. The main tool is a Lagrangian representation introduced by the second author, which allows to decompose the energy along characteristic curves.
{"title":"Stability of the vortex in micromagnetics and related models","authors":"X. Lamy, E. Marconi","doi":"10.2422/2036-2145.202209_012","DOIUrl":"https://doi.org/10.2422/2036-2145.202209_012","url":null,"abstract":"We consider line-energy models of Ginzburg-Landau type in a two-dimensional simply-connected bounded domain. Configurations of vanishing energy have been characterized by Jabin, Otto and Perthame: the domain must be a disk, and the configuration a vortex. We prove a quantitative version of this statement in the class of $C^{1,1}$ domains, improving on previous results by Lorent. In particular, the deviation of the domain from a disk is controlled by a power of the energy, and that power is optimal. The main tool is a Lagrangian representation introduced by the second author, which allows to decompose the energy along characteristic curves.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"82 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83970088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-11DOI: 10.2422/2036-2145.202006_016
M. Graf, M. Kunzinger, Darko Mitrovich
. We prove existence of weak solutions to the Cauchy problem cor- responding to various strictly parabolic equations on a compact Riemannian manifold ( M,g ). This also includes strictly parabolic equations with stochas- tic forcing with linear diffusion. Existence is proved through a variant of the Galerkin method and can be used to construct a convergent finite element method.
{"title":"Galerkin-type methods for strictly parabolic equations on compact Riemannian manifolds","authors":"M. Graf, M. Kunzinger, Darko Mitrovich","doi":"10.2422/2036-2145.202006_016","DOIUrl":"https://doi.org/10.2422/2036-2145.202006_016","url":null,"abstract":". We prove existence of weak solutions to the Cauchy problem cor- responding to various strictly parabolic equations on a compact Riemannian manifold ( M,g ). This also includes strictly parabolic equations with stochas- tic forcing with linear diffusion. Existence is proved through a variant of the Galerkin method and can be used to construct a convergent finite element method.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86770307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-08DOI: 10.2422/2036-2145.202209_007
Cerf Raphael, Mariconda Carlo
Let $L:mathbb Rtimes mathbb Rto [0, +infty[,cup{+infty}$ be a Borel function. We consider the problem begin{equation}tag{P}min F(y)=int_0^1L(y(t), y'(t)),dt: y(0)=0,, yin W^{1,1}([0,1],mathbb R).end{equation} We give an example of a real valued Lagrangian $L$ for which the Lavrentiev phenomenon occurs. We state a condition, involving only the behavior of $L$ on the graph of two functions, that ensures the non-occurrence of the phenomenon. Our criterium weakens substantially the well-known condition, that $L$ is bounded on bounded sets.
{"title":"Occurrence of gap for one-dimensional scalar autonomous functionals with one end point condition","authors":"Cerf Raphael, Mariconda Carlo","doi":"10.2422/2036-2145.202209_007","DOIUrl":"https://doi.org/10.2422/2036-2145.202209_007","url":null,"abstract":"Let $L:mathbb Rtimes mathbb Rto [0, +infty[,cup{+infty}$ be a Borel function. We consider the problem begin{equation}tag{P}min F(y)=int_0^1L(y(t), y'(t)),dt: y(0)=0,, yin W^{1,1}([0,1],mathbb R).end{equation} We give an example of a real valued Lagrangian $L$ for which the Lavrentiev phenomenon occurs. We state a condition, involving only the behavior of $L$ on the graph of two functions, that ensures the non-occurrence of the phenomenon. Our criterium weakens substantially the well-known condition, that $L$ is bounded on bounded sets.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"207 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77247771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-07DOI: 10.2422/2036-2145.202209_004
M. Bhupal, B. Ozbagci
In a previous work, we proved that each minimal symplectic filling of any oriented lens space, viewed as the singularity link of some cyclic quotient singularity and equipped with its canonical contact structure, can be obtained from the minimal resolution of the singularity by a sequence of symplectic rational blowdowns along linear plumbing graphs. Here we give a dramatically simpler visual presentation of our rational blowdown algorithm in terms of the triangulations of a convex polygon. As a consequence, we are able to organize the symplectic deformation equivalence classes of all minimal symplectic fillings of any given lens space equipped with its canonical contact structure, as a graded, directed, rooted, and connected graph, where the root is the minimal resolution of the corresponding cyclic quotient singularity and each directed edge is a symplectic rational blowdown along an explicit linear plumbing graph. Moreover, we provide an upper bound for the rational blowdown depth of each minimal symplectic filling.
{"title":"Rational blowdown graphs for symplectic fillings of lens spaces","authors":"M. Bhupal, B. Ozbagci","doi":"10.2422/2036-2145.202209_004","DOIUrl":"https://doi.org/10.2422/2036-2145.202209_004","url":null,"abstract":"In a previous work, we proved that each minimal symplectic filling of any oriented lens space, viewed as the singularity link of some cyclic quotient singularity and equipped with its canonical contact structure, can be obtained from the minimal resolution of the singularity by a sequence of symplectic rational blowdowns along linear plumbing graphs. Here we give a dramatically simpler visual presentation of our rational blowdown algorithm in terms of the triangulations of a convex polygon. As a consequence, we are able to organize the symplectic deformation equivalence classes of all minimal symplectic fillings of any given lens space equipped with its canonical contact structure, as a graded, directed, rooted, and connected graph, where the root is the minimal resolution of the corresponding cyclic quotient singularity and each directed edge is a symplectic rational blowdown along an explicit linear plumbing graph. Moreover, we provide an upper bound for the rational blowdown depth of each minimal symplectic filling.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85415751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-28DOI: 10.2422/2036-2145.202107_004
H. Hamada, G. Kohr
{"title":"Loewner PDE, inverse Loewner chains and nonlinear resolvents of the Carathéodory family in infinite dimensions","authors":"H. Hamada, G. Kohr","doi":"10.2422/2036-2145.202107_004","DOIUrl":"https://doi.org/10.2422/2036-2145.202107_004","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80589048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-28DOI: 10.2422/2036-2145.202202_011
Alexandre Arias Junior, A. Ascanelli, M. Cappiello
{"title":"On the quantitative isoperimetric inequality in the plane with the barycentric asymmetry","authors":"Alexandre Arias Junior, A. Ascanelli, M. Cappiello","doi":"10.2422/2036-2145.202202_011","DOIUrl":"https://doi.org/10.2422/2036-2145.202202_011","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86975868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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