ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE最新文献

{"title":"A representation formula for members of SBV dual","authors":"Philippe Bouafia, T. Pauw","doi":"10.2422/2036-2145.202110_011","DOIUrl":"https://doi.org/10.2422/2036-2145.202110_011","url":null,"abstract":"We give an integral representation formula for members of the dual ofSBV (R) in terms of functions that are defined on R̂, an appropriate fiber space that we introduce, consisting of pairs (x, [E ]x ) where [E ]x is an approximate germ of an (n−1)-rectifiable set E at x.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73031419","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}

{"title":"Generalized Stallings' decomposition theorems for pro-p groups","authors":"Mattheus Aguiar, P. Zalesski","doi":"10.2422/2036-2145.202111_011","DOIUrl":"https://doi.org/10.2422/2036-2145.202111_011","url":null,"abstract":"The celebrated Stallings' decomposition theorem states that the splitting of a finite index subgroup $H$ of a finitely generated group $G$ as an amalgamated free product or an HNN-extension over a finite group implies the same for $G$. We generalize the pro-$p$ version of it proved by Weigel and the second author to splittings over infinite pro-$p$ groups. This generalization does not have any abstract analogs. We also prove that generalized accessibility of finitely generated pro-$p$ groups is closed for commensurability.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91543212","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}

{"title":"Backward Rauzy-Veech algorithm and horizontal saddle connections","authors":"Przemysław Berk","doi":"10.2422/2036-2145.202110_010","DOIUrl":"https://doi.org/10.2422/2036-2145.202110_010","url":null,"abstract":"We study the combinatorial and dynamical properties of translations surfaces with horizontal saddle connections from the point of view of backward Rauzy-Veech induction. Namely, we prove that although the horizontal saddle connections do not rule out existence of the infinite orbit under backward Rauzy-Veech algorithm, they disallow the ∞completeness of such orbit. Furthermore, we prove that if an orbit under backward Rauzy-Veech algorithm is infinite, then the minimality of the horizontal translation flow is equivalent to the eventual appearance of all horizontal saddle connections as sides of the polygonal represenation of a surface. The main goal of this note is to study the relations between horizontal saddle connections and the combinatorics of the inverse RauzyVeech algorithm for translation surfaces as well as dynamics of the horizontal translation flows. In [2] (Proposition 4.3) Marmi, Ulcigrai and Yoccoz prove that if a translation surface does not have horizontal saddle connections, then its backward Rauzy-Veech induction orbit is indefinitely well-defined and ∞-complete, that is every symbol is a backward winner infinitely many times. In the same article the authors pose a question, whether these two conditions are equivalent. We answer affirmatively to this question in Theorem 11. The proof utilizes only combinatorics and geometry of translation surfaces. However, before proving Theorem 11, we prove Proposition 7 which states that, typically, possessing horizontal saddle connections does not rule out that the backward orbit with respect to the inverse RauzyVeech algorithm is well defined. Moreover, in Theorem 12 we prove that appearance of horizontal connections as sides of polygonal representations of translations surfaces is closely tied to the minimality of the horizontal translation flow. More precisely, we show that the horizontal translation flow is minimal if and only if all (if any) horizontal saddle connections appear as sides of a polygonal representation of a surface after applying a finite number of backward Rauzy-Veech induction steps. MSC CLASSIFICATION: 37E05, 37E35 1 ar X iv :2 10 9. 13 69 1v 2 [ m at h. D S] 2 3 Fe b 20 22 P. BERK HORIZONTAL SADDLE CONNECTIONS Acknowledgments: The author would like to thank Corinna Ulcigrai for pointing out the problem and her continuous support and Frank Trujillo for many useful remarks. The research that lead to this result was supported by Swiss National Science Foundation Grant 200021 188617/1 and Narodowe Centrum Nauki Grant OPUS 142017/27/B/ST1/00078. 1. Interval exchange transformations and translations surfaces We recall first basic notions and properties related to IETs and translation surfaces. Let A be an alphabet of #A ≥ 2 elements. For more information and basic properties, including the ergodic properties of interval exchange transformations, translation surfaces and Rauzy-Veech algorithm we refer the reader e.g. to [4] and [5]. Let SA 0 :={π = (π0, π1) : A → {1, . . . ,","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87524355","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}

{"title":"Fractional integration of summable functions: Maz'ya's~$Phi$-inequalities","authors":"D. Stolyarov","doi":"10.2422/2036-2145.202110_001","DOIUrl":"https://doi.org/10.2422/2036-2145.202110_001","url":null,"abstract":"We study the inequalities of the type $|int_{mathbb{R}^d} Phi(K*f)| lesssim |f|_{L_1(mathbb{R}^d)}^p$, where the kernel $K$ is homogeneous of order $alpha - d$ and possibly vector-valued, the function $Phi$ is positively $p$-homogeneous, and $p = d/(d-alpha)$. Under mild regularity assumptions on $K$ and $Phi$, we find necessary and sufficient conditions on these functions under which the inequality holds true with a uniform constant for all sufficiently regular functions $f$.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83137310","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}

{"title":"Almost sharp descriptions of traces of Sobolev $W_{p}^{1}(mathbb{R}^{n})$-spaces to arbitrary compact subsets of $mathbb{R}^{n}$","authors":"A. Tyulenev","doi":"10.2422/2036-2145.202109_027","DOIUrl":"https://doi.org/10.2422/2036-2145.202109_027","url":null,"abstract":"Let $S subset mathbb{R}^{n}$ be an arbitrary nonempty compact set such that the $d$-Hausdorff content $mathcal{H}^{d}_{infty}(S)>0$ for some $d in (0,n]$. For each $p in (max{1,n-d},n]$, an almost sharp intrinsic description of the trace space $W_{p}^{1}(mathbb{R}^{n})|_{S}$ of the Sobolev space $W_{p}^{1}(mathbb{R}^{n})$ to the set $S$ is obtained. Furthermore, for each $p in (max{1,n-d},n]$ and $varepsilon in (0, min{p-(n-d),p-1})$, new bounded linear extension operators from the trace space $W_{p}^{1}(mathbb{R}^{n})|_{S}$ into the space $W_{p-varepsilon}^{1}(mathbb{R}^{n})$ are constructed.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73231359","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}

{"title":"Vaisman theorem for LCK spaces","authors":"Ovidiu Preda, Miron Stanciu","doi":"10.2422/2036-2145.202201_006","DOIUrl":"https://doi.org/10.2422/2036-2145.202201_006","url":null,"abstract":". Vaisman’s theorem for locally conformally K¨ahler (lcK) compact manifolds states that any lcK metric on a compact complex manifold which admits a K¨ahler metric is, in fact, globally conformally K¨ahler (gcK). In this paper, we extend this theorem to compact complex spaces with singularities. PN-III-P1-1.1-TE-2019-0262, within PNCDI III. Miron Stanciu was partially supported by a grant of Ministry of Research and Inno-vation, CNCS - UEFISCDI, project no. PN-III-P4-ID-PCE-2020-0025, within PNCDI III.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"228 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82265728","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}

{"title":"On the regularity theory for mixed local and nonlocal quasilinear parabolic equations","authors":"Prashanta Garain, J. Kinnunen","doi":"10.2422/2036-2145.202110_006","DOIUrl":"https://doi.org/10.2422/2036-2145.202110_006","url":null,"abstract":"Abstract. We consider mixed local and nonlocal quasilinear parabolic equations of p-Laplace type and discuss several regularity properties of weak solutions for such equations. More precisely, we establish local boundeness of weak subsolutions, local Hölder continuity of weak solutions, lower semicontinuity of weak supersolutions as well as upper semicontinuity of weak subsolutions. We also discuss the pointwise behavior of the semicontinuous representatives. Our main results are valid for sign changing solutions. Our approach is purely analytic and is based on energy estimates and the De Giorgi theory.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86351491","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}

{"title":"Holomorphic convexity of pseudoconvex surfaces","authors":"Viorel Vîjîitu","doi":"10.2422/2036-2145.202011_018","DOIUrl":"https://doi.org/10.2422/2036-2145.202011_018","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"93 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76564710","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}

{"title":"Propriétés de la hauteur de Faltings","authors":"Gaël Rémond","doi":"10.2422/2036-2145.202010_062","DOIUrl":"https://doi.org/10.2422/2036-2145.202010_062","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78947802","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}

{"title":"Alexander invariants and cohomology jump loci in group extensions","authors":"Alexander I. Suciu","doi":"10.21203/rs.3.rs-912019/v1","DOIUrl":"https://doi.org/10.21203/rs.3.rs-912019/v1","url":null,"abstract":"\u0000 We study the integral, rational, and modular Alexander invariants, as well as the cohomology jump loci of groups arising as extensions with trivial algebraic monodromy. Our focus is on extensions of the form 1→K→G→Q→1, where Q is an abelian group acting trivially on H1(K;ℤ), with suitable modifications in the rational and mod-p settings. We find a tight relationship between the Alexander invariants, the characteristic varieties, and the resonance varieties of the groups K and G. This leads to an inequality between the respective Chen ranks, which becomes an equality in degrees greater than 1 for split extensions.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91024880","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}