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Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze最新文献

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Spectral analysis for some third-order differential equations: a semigroup approach 一些三阶微分方程的谱分析:半群方法
2区 数学
Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze Pub Date : 2023-10-25 DOI: 10.2422/2036-2145.202212_003
Flank D. M. Bezerra, Alexandre N. Carvalho, Lucas A. Santos, Carlos R. Takaessu jr
{"title":"Spectral analysis for some third-order differential equations: a semigroup approach","authors":"Flank D. M. Bezerra, Alexandre N. Carvalho, Lucas A. Santos, Carlos R. Takaessu jr","doi":"10.2422/2036-2145.202212_003","DOIUrl":"https://doi.org/10.2422/2036-2145.202212_003","url":null,"abstract":"","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"6 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135168408","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}
引用次数: 0
Higgs bundles and flat connections over compact Sasakian manifolds, II: quasi-regular bundles 紧化Sasakian流形上的Higgs束和平面连接，II:拟正则束
2区 数学
Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze Pub Date : 2023-10-25 DOI: 10.2422/2036-2145.202203_024
Indranil Biswas, Hisashi Kasuya
{"title":"Higgs bundles and flat connections over compact Sasakian manifolds, II: quasi-regular bundles","authors":"Indranil Biswas, Hisashi Kasuya","doi":"10.2422/2036-2145.202203_024","DOIUrl":"https://doi.org/10.2422/2036-2145.202203_024","url":null,"abstract":"In this continuation of cite{BK} we investigate the non-abelian Hodge correspondence on compact Sasakian manifolds with emphasis on the quasi-regular case. On quasi-regular Sasakian manifolds, we introduce the notions of quasi-regularity and regularity of basic vector bundles. These notions are useful in relating the vector bundles over a quasi-regular Sasakian manifold with the orbibundles over the orbifold defined by the orbits of the Reeb foliation of the Sasakian manifold. We note that the non-abelian Hodge correspondence on quasi-regular Sasakian manifolds gives a canonical correspondence between the semi-simple representations of the orbifold fundamental groups and the Higgs orbibundles on locally cyclic complex orbifolds admitting Hodge metrics. Under the quasi-regularity of Sasakian manifolds and vector bundles, we extend this correspondence to one between the flat bundles and the basic Higgs bundles. We also prove a Sasakian analogue of the characterization of numerically flat bundles given by Demailly, Peternell and Schneider.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135169046","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}
引用次数: 2
Reading analytic invariants of parabolic diffeomorphisms from their orbits 从抛物线微分同态的轨道读出解析不变量
2区 数学
Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze Pub Date : 2023-10-25 DOI: 10.2422/2036-2145.202208_022
Martin Klimeš, Pavao Mardešić, Goran Radunović, Maja Resman
{"title":"Reading analytic invariants of parabolic diffeomorphisms from their orbits","authors":"Martin Klimeš, Pavao Mardešić, Goran Radunović, Maja Resman","doi":"10.2422/2036-2145.202208_022","DOIUrl":"https://doi.org/10.2422/2036-2145.202208_022","url":null,"abstract":"In this paper we study germs of diffeomorphisms in the complex plane. We address the following problem: How to read a diffeomorphism $f$ knowing one of its orbits $mathbb{A}$? We solve this problem for parabolic germs. This is done by associating to the orbit ${mathbb{A}}$ a function that we call the dynamic theta function $Theta_{mathbb{A}}$. We prove that the function $Theta_{mathbb{A}}$ is $2pi imathbb{Z}$-resurgent. We show that one can obtain the sectorial Fatou coordinate as a Laplace-type integral transform of the function $Theta_{mathbb{A}}$. This enables one to read the analytic invariants of a diffeomorphism from the theta function of one of its orbits. We also define a closely related fractal theta function $tilde{Theta}_{mathbb{A}}$, which is inspired by and generalizes the geometric zeta function of a fractal string, and show that it also encodes the analytic invariants of the diffeomorphism.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135166563","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}
引用次数: 0
Dirichlet forms on metric measure spaces as Mosco limits of Korevaar-Schoen energies 度量度量空间上的狄利克雷形式为korevar - schoen能量的Mosco极限
2区 数学
Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze Pub Date : 2023-10-25 DOI: 10.2422/2036-2145.202302_013
Patricia Alonso Ruiz, Fabrice Baudoin
{"title":"Dirichlet forms on metric measure spaces as Mosco limits of Korevaar-Schoen energies","authors":"Patricia Alonso Ruiz, Fabrice Baudoin","doi":"10.2422/2036-2145.202302_013","DOIUrl":"https://doi.org/10.2422/2036-2145.202302_013","url":null,"abstract":"This paper establishes sufficient general conditions for the existence of Mosco limits of Korevaar-Schoen $L^2$ energies, first in the context of Cheeger spaces and then in the context of fractal-like spaces with walk dimension greater than 2. Among the ingredients, a new Rellich-Kondrachov type theorem for Korevaar-Schoen-Sobolev spaces is of independent interest.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135166692","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}
引用次数: 0
On elliptic equations involving surface measures 关于涉及曲面测度的椭圆方程
2区 数学
Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze Pub Date : 2023-10-25 DOI: 10.2422/2036-2145.202303_012
Marius Müller
{"title":"On elliptic equations involving surface measures","authors":"Marius Müller","doi":"10.2422/2036-2145.202303_012","DOIUrl":"https://doi.org/10.2422/2036-2145.202303_012","url":null,"abstract":"We show optimal Lipschitz regularity for very weak solutions of the (measure-valued) elliptic PDE $-mathrm{div}(A(x) nabla u) = Q ; mathcal{H}^{n-1} llcorner Gamma$ in a smooth domain $Omega subset mathbb{R}^n$. Here $Gamma$ is a $C^{1,alpha}$-regular hypersurface, $Qin C^{0,alpha}$ is a density on $Gamma$, and the coefficient matrix $A$ is symmetric, uniformly elliptic and $W^{1,q}$-regular $(q>n)$. We also discuss optimality of these assumptions on the data. The equation can be understood as a special coupling of two $A$-harmonic functions with an interface $Gamma$. As such it plays an important role in several free boundary problems, as we shall discuss.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"24 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135169357","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}
引用次数: 2
Maps of bounded variation from PI spaces to metric spaces 从PI空间到度量空间的有界变化的映射
2区 数学
Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze Pub Date : 2023-10-25 DOI: 10.2422/2036-2145.202307_003
Camillo Brena, Francesco Nobili, Enrico Pasqualetto
{"title":"Maps of bounded variation from PI spaces to metric spaces","authors":"Camillo Brena, Francesco Nobili, Enrico Pasqualetto","doi":"10.2422/2036-2145.202307_003","DOIUrl":"https://doi.org/10.2422/2036-2145.202307_003","url":null,"abstract":"We study maps of bounded variation defined on a metric measure space and valued into a metric space. Assuming the source space to satisfy a doubling and Poincar'e property, we produce a well-behaved relaxation theory via approximation by simple maps. Moreover, several equivalent characterizations are given, including a notion in weak duality with test plans.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"21 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135166691","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}
引用次数: 3
Modulus of continuity of weak solutions to a class of singular elliptic equations 一类奇异椭圆型方程弱解的连续模
2区 数学
Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze Pub Date : 2023-10-25 DOI: 10.2422/2036-2145.202211_020
Xiangsheng Xu
{"title":"Modulus of continuity of weak solutions to a class of singular elliptic equations","authors":"Xiangsheng Xu","doi":"10.2422/2036-2145.202211_020","DOIUrl":"https://doi.org/10.2422/2036-2145.202211_020","url":null,"abstract":"In this paper we study the modulus of continuity of weak solutions to a singular elliptic equation in the plane under very weak assumption on the integrability of the elliptic coefficients. Our investigation reveals that the modulus of continuity can be described by the reciprocal of the logarithmic function raised to a power. However, the power can be arbitrarily large. This is in sharp contrast with a result by J. Onninen and X. Zhong for a degenerate elliptic equation in the plane, in which the power must be suitably small.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"39 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135166693","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}
引用次数: 1
The structure of the homogeneous Riemannian manifolds with nullity 具有零的齐次黎曼流形的结构
2区 数学
Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze Pub Date : 2023-10-25 DOI: 10.2422/2036-2145.202210_003
Antonio J. Di Scala, Carlos E. Olmos, Francisco Vittone
{"title":"The structure of the homogeneous Riemannian manifolds with nullity","authors":"Antonio J. Di Scala, Carlos E. Olmos, Francisco Vittone","doi":"10.2422/2036-2145.202210_003","DOIUrl":"https://doi.org/10.2422/2036-2145.202210_003","url":null,"abstract":"","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"131 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135166696","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}
引用次数: 0
Manifolds with trivial Chern classes I: hyperelliptic manifolds and question by Severi 具有平凡陈类的流形I:超椭圆流形与Severi的问题
2区 数学
Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze Pub Date : 2023-10-25 DOI: 10.2422/2036-2145.202303_017
Fabrizio Catanese
{"title":"Manifolds with trivial Chern classes I: hyperelliptic manifolds and question by Severi","authors":"Fabrizio Catanese","doi":"10.2422/2036-2145.202303_017","DOIUrl":"https://doi.org/10.2422/2036-2145.202303_017","url":null,"abstract":"","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135166699","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}
引用次数: 0
Stability vs.~instability of singular steady states in the parabolic-elliptic Keller-Segel system on $R^n$ R^n$上抛物-椭圆Keller-Segel系统奇异稳态的稳定性与不稳定性
2区 数学
Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze Pub Date : 2023-10-25 DOI: 10.2422/2036-2145.202303_006
Francesca Colasuonno, Michael Winkler
{"title":"Stability vs.~instability of singular steady states in the parabolic-elliptic Keller-Segel system on $R^n$","authors":"Francesca Colasuonno, Michael Winkler","doi":"10.2422/2036-2145.202303_006","DOIUrl":"https://doi.org/10.2422/2036-2145.202303_006","url":null,"abstract":"","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"196 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135166690","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}
引用次数: 0
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