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Illinois Journal of Mathematics最新文献

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A real-variable construction with applications to BMO–Teichmüller theory 一个实变量构造及其在BMO–Teichmüller理论中的应用
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-07-21 DOI: 10.1215/00192082-10036297
Huaying Wei, M. Zinsmeister
{"title":"A real-variable construction with applications to BMO–Teichmüller theory","authors":"Huaying Wei, M. Zinsmeister","doi":"10.1215/00192082-10036297","DOIUrl":"https://doi.org/10.1215/00192082-10036297","url":null,"abstract":"With the use of real-variable techniques, we construct a weight function ω on the interval [0, 2π) that is doubling and satisfies logω is a BMO function, but which is not a Muckenhoupt weight (A∞). Applications to the BMO-Teichmüller space and the space of chord-arc curves are considered.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43235760","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}
引用次数: 1
Primality of weakly connected collections of cells and weakly closed path polyominoes 弱连通集合的素性与弱闭路径多面体
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-06-03 DOI: 10.1215/00192082-10123611
Carmelo Cisto, F. Navarra, R. Utano
{"title":"Primality of weakly connected collections of cells and weakly closed path polyominoes","authors":"Carmelo Cisto, F. Navarra, R. Utano","doi":"10.1215/00192082-10123611","DOIUrl":"https://doi.org/10.1215/00192082-10123611","url":null,"abstract":"In this paper we study the primality of weakly connected collections of cells, showing that the ideal generated by inner 2-minors attached to a weakly connected and simple collection of cells is the toric ideal of the edge ring of a weakly chordal bipartite graph. As an application of this result we characterize the primality of the polyomino ideals of weakly closed paths, a new class of non simple polyominoes.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42729153","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}
引用次数: 4
Orbifolds having Euler number zero Heegaard decomposition 具有零Euler数Heegaard分解的Orbifolds
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-05-01 DOI: 10.1215/00192082-9252453
J. Kalliongis, R. Ohashi
{"title":"Orbifolds having Euler number zero Heegaard decomposition","authors":"J. Kalliongis, R. Ohashi","doi":"10.1215/00192082-9252453","DOIUrl":"https://doi.org/10.1215/00192082-9252453","url":null,"abstract":"In this paper, we completely classify, up to homeomorphism, the orientable and nonorientable orbifolds which have a Heegaard decomposition consisting of orbifold handlebodies with Euler number zero. In addition we compute their fundamental groups.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"65 1","pages":"339-384"},"PeriodicalIF":0.6,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42958822","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}
引用次数: 0
Approximating spaces of Nagata dimension zero by weighted trees 用加权树逼近Nagata维数为零的空间
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-04-28 DOI: 10.1215/00192082-10414720
Giuliano Basso, H. Sidler
{"title":"Approximating spaces of Nagata dimension zero by weighted trees","authors":"Giuliano Basso, H. Sidler","doi":"10.1215/00192082-10414720","DOIUrl":"https://doi.org/10.1215/00192082-10414720","url":null,"abstract":"We prove that if a metric space $X$ has Nagata dimension zero with constant $c$, then there exists a dense subset of $X$ that is $8c$-bilipschitz equivalent to a weighted tree. The factor $8$ is the best possible if $c=1$, that is, if $X$ is an ultrametric space. This yields a new proof of a result of Chan, Xia, Konjevod and Richa. Moreover, as an application, we also obtain quantitative versions of certain metric embedding and Lipschitz extension results of Lang and Schlichenmaier. Finally, we prove a variant of our main theorem for $0$-hyperbolic proper metric spaces. This generalizes a result of Gupta.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45664028","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}
引用次数: 2
Metric equivalences of Heintze groups and applications to classifications in low dimension Heintze群的度量等价性及其在低维分类中的应用
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-04-01 DOI: 10.1215/00192082-9702295
Ville Kivioja, E. Donne, Sebastiano Golo
{"title":"Metric equivalences of Heintze groups and applications to classifications in low dimension","authors":"Ville Kivioja, E. Donne, Sebastiano Golo","doi":"10.1215/00192082-9702295","DOIUrl":"https://doi.org/10.1215/00192082-9702295","url":null,"abstract":"We approach the quasi-isometric classification questions on Lie groups by considering low dimensional cases and isometries alongside quasi-isometries. First, we present some new results related to quasi-isometries between Heintze groups. Then we will see how these results together with the existing tools related to isometries can be applied to groups of dimension 4 and 5 in particular. Thus we take steps towards determining all the equivalence classes of groups up to isometry and quasi-isometry. We completely solve the classification up to isometry for simply connected solvable groups in dimension 4, and for the subclass of groups of polynomial growth in dimension 5.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47717790","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}
引用次数: 1
Counterexamples to Lp collapsing estimates Lp崩溃估计的反例
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-04-01 DOI: 10.1215/00192082-8886967
Xiumin Du, M. Machedon
{"title":"Counterexamples to Lp collapsing estimates","authors":"Xiumin Du, M. Machedon","doi":"10.1215/00192082-8886967","DOIUrl":"https://doi.org/10.1215/00192082-8886967","url":null,"abstract":"We show that certain L2 space-time estimates for generalized density matrices which have been used by several authors in recent years to study equations of BBGKY or Hartree-Fock type, do not have non-trivial LpLq generalizations.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"65 1","pages":"191-200"},"PeriodicalIF":0.6,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49425993","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}
引用次数: 0
Configuration spaces, multijet transversality, and the square-peg problem 构型空间、多射流横截面和方桩问题
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-03-12 DOI: 10.1215/00192082-10120454
J. Cantarella, E. Denne, J. McCleary
{"title":"Configuration spaces, multijet transversality, and the square-peg problem","authors":"J. Cantarella, E. Denne, J. McCleary","doi":"10.1215/00192082-10120454","DOIUrl":"https://doi.org/10.1215/00192082-10120454","url":null,"abstract":"A BSTRACT . We prove a transversality “lifting property” for compactified configuration spaces as an application of the multijet transversality theorem: given a submanifold of configurations of points on an embedding of a compact manifold M in Euclidean space, we can find a dense set of smooth embeddings of M for which the corresponding configuration space of points is transverse to any submanifold of the configuration space of points in Euclidean space, as long as the two submanifolds of compactified configuration space are boundary-disjoint. We use this setup to provide an attractive proof of the square-peg problem: there is a dense family of smoothly embedded circles in the plane where each simple closed curve has an odd number of inscribed squares, and there is a dense family of smoothly embedded circles in R n where each simple closed curve has an odd number of inscribed square-like quadrilaterals.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46581337","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}
引用次数: 3
Global automorphic Sobolev theory and the automorphic heat kernel 全局自同构Sobolev理论与自同构热核
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-02-20 DOI: 10.1215/00192082-9082091
A. DeCelles
{"title":"Global automorphic Sobolev theory and the automorphic heat kernel","authors":"A. DeCelles","doi":"10.1215/00192082-9082091","DOIUrl":"https://doi.org/10.1215/00192082-9082091","url":null,"abstract":"Heat kernels arise in a variety of contexts including probability, geometry, and functional analysis; the automorphic heat kernel is particularly important in number theory and string theory. The typical construction of an automorphic heat kernel as a Poincare series presents analytic difficulties, which can be dealt with in special cases (e.g. hyperbolic spaces) but are often sidestepped in higher rank by restricting to the compact quotient case. In this paper, we present a new approach, using global automorphic Sobolev theory, a robust framework for solving automorphic PDEs that does not require any simplifying assumptions about the rank of the symmetric space or the compactness of the arithmetic quotient. We construct an automorphic heat kernel via its automorphic spectral expansion in terms of cusp forms, Eisenstein series, and residues of Eisenstein series. We then prove uniqueness of the automorphic heat kernel as an application of operator semigroup theory. Finally, we prove the smoothness of the automorphic heat kernel by proving that its automorphic spectral expansion converges in the $C^infty$-topology.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49608303","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}
引用次数: 1
Rees algebra and special fiber ring of binomial edge ideals of closed graphs 闭图二项式边理想的Rees代数和特殊纤维环
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-02-05 DOI: 10.1215/00192082-9702270
Arvind Kumar
{"title":"Rees algebra and special fiber ring of binomial edge ideals of closed graphs","authors":"Arvind Kumar","doi":"10.1215/00192082-9702270","DOIUrl":"https://doi.org/10.1215/00192082-9702270","url":null,"abstract":"In this article, we compute the regularity of Rees algebra of binomial edge ideals of closed graphs. We obtain a lower bound for the regularity of Rees algebra of binomial edge ideals. We also study some algebraic properties of the Rees algebra and special fiber ring of binomial edge ideals of closed graphs via algebraic properties of their initial algebra and Sagbi basis theory. We obtain an upper bound for the regularity of the special fiber ring of binomial edge ideals of closed graphs.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43397937","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}
引用次数: 4
A gradient estimate for the Monge–Ampère equation on compact almost Hermitian manifolds 紧几乎Hermitian流形上Monge–Ampère方程的梯度估计
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1215/00192082-9591203
Masaya Kawamura
{"title":"A gradient estimate for the Monge–Ampère equation on compact almost Hermitian manifolds","authors":"Masaya Kawamura","doi":"10.1215/00192082-9591203","DOIUrl":"https://doi.org/10.1215/00192082-9591203","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45712990","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}
引用次数: 0
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