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Annals of Global Analysis and Geometry最新文献

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Estimates of Kähler metrics on noncompact finite volume hyperbolic Riemann surfaces, and their symmetric products 非紧凑有限体积双曲黎曼曲面上的凯勒度量及其对称积的估算
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-09-25 DOI: 10.1007/s10455-024-09967-8
Anilatmaja Aryasomayajula, Arijit Mukherjee
{"title":"Estimates of Kähler metrics on noncompact finite volume hyperbolic Riemann surfaces, and their symmetric products","authors":"Anilatmaja Aryasomayajula,&nbsp;Arijit Mukherjee","doi":"10.1007/s10455-024-09967-8","DOIUrl":"10.1007/s10455-024-09967-8","url":null,"abstract":"<div><p>Let <i>X</i> denote a noncompact finite volume hyperbolic Riemann surface of genus <span>(gge 2)</span>, with only one puncture at <span>(iinfty )</span> (identifying <i>X</i> with its universal cover <span>({mathbb {H}})</span>). Let <span>({{{overline{X}}}}:=Xcup lbrace iinfty rbrace )</span> denote the Satake compactification of <i>X</i>. Let <span>(Omega _{{{{overline{X}}}}})</span> denote the cotangent bundle on <span>({{{overline{X}}}})</span>. For <span>(kgg 1)</span>, we derive an estimate for <span>(mu _{{ {overline{X}}}}^{textrm{Ber},{{k}}})</span>, the Bergman metric associated to the line bundle <span>({{mathcal {L}}}^{k}:=Omega _{{{{overline{X}}}}}^{otimes {{k}}}otimes {{mathcal {O}}}_{{{{overline{X}}}}}((k-1)iinfty ))</span>. For a given <span>(dge 1)</span>, the pull-back of the Fubini-Study metric on the Grassmannian, which we denote by <span>(mu _{textrm{Sym}^{{d}}({{overline{X}}})}^{textrm{FS},k})</span>, defines a Kähler metric on <span>(textrm{Sym}^{{d}}({{overline{X}}}))</span>, the <i>d</i>-fold symmetric product of <span>({{{overline{X}}}})</span>. Using our estimates of <span>(mu _{{ {overline{X}}}}^{textrm{Ber},{{k}}})</span>, as an application, we derive an estimate for <span>(mu _{textrm{Sym}^{{d}}({{overline{X}}}),textrm{vol}}^{textrm{FS},k})</span>, the volume form associated to the (1,1)-form <span>(mu _{textrm{Sym}^{{d}}({{overline{X}}})}^{textrm{FS},k})</span>.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 effects of the null energy condition on totally umbilic hypersurfaces in a class of static spacetimes 论一类静态空间中完全脐状超曲面的空能条件效应
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-09-16 DOI: 10.1007/s10455-024-09969-6
Markus Wolff
{"title":"On effects of the null energy condition on totally umbilic hypersurfaces in a class of static spacetimes","authors":"Markus Wolff","doi":"10.1007/s10455-024-09969-6","DOIUrl":"10.1007/s10455-024-09969-6","url":null,"abstract":"<div><p>We study the effects of the null energy condition on totally umbilic hypersurfaces in a class of static spacetimes, both in the spacelike and the timelike case, respectively. In the spacelike case, we study totally umbilic warped product graphs and give a full characterization of embedded surfaces with constant spacetime mean curvature using an Alexandrov Theorem by Brendle and Borghini–Fogagnolo–Pinamonti. In the timelike case, we achieve a characterization of photon surfaces with constant umbilicity factor similar to a result by Cederbaum–Galloway.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-024-09969-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Locally constrained inverse curvature flow and Hu–Li’s conjecture 局部约束反曲率流和胡李猜想
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-09-05 DOI: 10.1007/s10455-024-09968-7
Kuicheng Ma
{"title":"Locally constrained inverse curvature flow and Hu–Li’s conjecture","authors":"Kuicheng Ma","doi":"10.1007/s10455-024-09968-7","DOIUrl":"10.1007/s10455-024-09968-7","url":null,"abstract":"<div><p>In this paper, an Alexandrov–Fenchel inequality is established for closed 2-convex spacelike hypersurface in de Sitter space by investigating the behavior of some locally constrained inverse curvature flow, which provides a partial answer to the conjecture raised by Hu and Li in (Adv Math 413:108826, 2023).</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Correction: The geometry of compact homogeneous spaces with two isotropy summands 更正：具有两个各向同性和子的紧凑同质空间的几何学
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-08-27 DOI: 10.1007/s10455-024-09966-9
William Dickinson, Megan M. Kerr
{"title":"Correction: The geometry of compact homogeneous spaces with two isotropy summands","authors":"William Dickinson,&nbsp;Megan M. Kerr","doi":"10.1007/s10455-024-09966-9","DOIUrl":"10.1007/s10455-024-09966-9","url":null,"abstract":"","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A comparison of the absolute and relative real analytic torsion forms 绝对和相对实解析扭转形式的比较
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-08-16 DOI: 10.1007/s10455-024-09965-w
Jialin Zhu
{"title":"A comparison of the absolute and relative real analytic torsion forms","authors":"Jialin Zhu","doi":"10.1007/s10455-024-09965-w","DOIUrl":"10.1007/s10455-024-09965-w","url":null,"abstract":"<div><p>In this paper we establish a comparison formula of the absolute and relative real analytic torsion forms over fibrations with boundaries. The key tool is a gluing formula of analytic torsion forms proved by Puchol and Zhang and the author. As a consequence of the comparison formula, we prove another version of the gluing formula of the analytic torsion forms conjectured by the author.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Extrinsic geometry and linear differential equations of (mathfrak {sl}_3)-type 外几何学和 $$mathfrak {sl}_3$ 型线性微分方程
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-08-06 DOI: 10.1007/s10455-024-09964-x
Boris Doubrov, Tohru Morimoto
{"title":"Extrinsic geometry and linear differential equations of (mathfrak {sl}_3)-type","authors":"Boris Doubrov,&nbsp;Tohru Morimoto","doi":"10.1007/s10455-024-09964-x","DOIUrl":"10.1007/s10455-024-09964-x","url":null,"abstract":"<div><p>As an application of the general theory on extrinsic geometry (Doubrov et al. in SIGMA Symmetry Integr Geom Methods Appl 17:061, 2021), we investigate extrinsic geometry in flag varieties and systems of linear PDE’s for a class of special interest associated with the adjoint representation of <span>(mathfrak {sl}(3))</span>. We carry out a complete local classification of the homogeneous structures in this class. As a result, we find 7 kinds of new systems of linear PDE’s of second order on a 3-dimensional contact manifold each of which has a solution space of dimension 8. Among them there are included a system of PDE’s called contact Cayley’s surface and one which has <span>(varvec{mathfrak {sl}}(2))</span> symmetry.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Schwartz correspondence for real motion groups in low dimensions 低维实运动群的施瓦茨对应关系
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-07-29 DOI: 10.1007/s10455-024-09963-y
Francesca Astengo, Bianca Di Blasio, Fulvio Ricci
{"title":"Schwartz correspondence for real motion groups in low dimensions","authors":"Francesca Astengo,&nbsp;Bianca Di Blasio,&nbsp;Fulvio Ricci","doi":"10.1007/s10455-024-09963-y","DOIUrl":"10.1007/s10455-024-09963-y","url":null,"abstract":"<div><p>For a Gelfand pair (<i>G</i>, <i>K</i>) with <i>G</i> a Lie group of polynomial growth and <i>K</i> a compact subgroup, the <i>Schwartz correspondence</i> states that the spherical transform maps the bi-<i>K</i>-invariant Schwartz space <span>({{mathcal {S}}}(Kbackslash G/K))</span> isomorphically onto the space <span>({{mathcal {S}}}(Sigma _{{mathcal {D}}}))</span>, where <span>(Sigma _{{mathcal {D}}})</span> is an embedded copy of the Gelfand spectrum in <span>({{mathbb {R}}}^ell )</span>, canonically associated to a generating system <span>({{mathcal {D}}})</span> of <i>G</i>-invariant differential operators on <i>G</i>/<i>K</i>, and <span>({{mathcal {S}}}(Sigma _{{mathcal {D}}}))</span> consists of restrictions to <span>(Sigma _{{mathcal {D}}})</span> of Schwartz functions on <span>({{mathbb {R}}}^ell )</span>. Schwartz correspondence is known to hold for a large variety of Gelfand pairs of polynomial growth. In this paper we prove that it holds for the strong Gelfand pair <span>((M_n,SO_n))</span> with <span>(n=3,4)</span>. The rather trivial case <span>(n=2)</span> is included in previous work by the same authors.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-024-09963-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141868769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A hyper-Kähler metric on the moduli spaces of monopoles with arbitrary symmetry breaking 具有任意对称破缺的单极子模空间上的超凯勒度量
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-07-16 DOI: 10.1007/s10455-024-09954-z
Jaime Mendizabal
{"title":"A hyper-Kähler metric on the moduli spaces of monopoles with arbitrary symmetry breaking","authors":"Jaime Mendizabal","doi":"10.1007/s10455-024-09954-z","DOIUrl":"10.1007/s10455-024-09954-z","url":null,"abstract":"<div><p>We construct the hyper-Kähler moduli space of framed monopoles over <span>(mathbb {R}^3)</span> for any connected, simply connected, compact, semisimple Lie group and arbitrary mass and charge, and hence arbitrary symmetry breaking. In order to do so, we define a configuration space of pairs with appropriate asymptotic conditions and perform an infinite-dimensional quotient construction. We make use of the b and scattering calculuses to study the relevant differential operators.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-024-09954-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141642576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Universal covers of non-negatively curved manifolds and formality 非负弯曲流形的普遍盖和形式性
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-07-04 DOI: 10.1007/s10455-024-09962-z
Aleksandar Milivojević
{"title":"Universal covers of non-negatively curved manifolds and formality","authors":"Aleksandar Milivojević","doi":"10.1007/s10455-024-09962-z","DOIUrl":"10.1007/s10455-024-09962-z","url":null,"abstract":"<div><p>We show that if the universal cover of a closed smooth manifold admitting a metric with non-negative Ricci curvature is formal, then the manifold itself is formal. We reprove a result of Fiorenza–Kawai–Lê–Schwachhöfer, that closed orientable manifolds with a non-negative Ricci curvature metric and sufficiently large first Betti number are formal. Our method allows us to remove the orientability hypothesis; we further address some cases of non-closed manifolds.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Left-invariant almost complex structures on the higher dimensional Kodaira–Thurston manifolds 高维柯达伊拉-瑟斯顿流形上的左变近复结构
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-06-25 DOI: 10.1007/s10455-024-09961-0
Tom Holt, Riccardo Piovani
{"title":"Left-invariant almost complex structures on the higher dimensional Kodaira–Thurston manifolds","authors":"Tom Holt,&nbsp;Riccardo Piovani","doi":"10.1007/s10455-024-09961-0","DOIUrl":"10.1007/s10455-024-09961-0","url":null,"abstract":"<div><p>We develop computational techniques which allow us to calculate the Kodaira dimension as well as the dimension of spaces of Dolbeault harmonic forms for left-invariant almost complex structures on the generalised Kodaira–Thurston manifolds.\u0000\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-024-09961-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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