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Annals of Global Analysis and Geometry最新文献

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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 0.7 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":"https://doi.org/10.1007/s10455-024-09969-6","url":null,"abstract":"<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>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","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":"","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 0.7 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":"https://doi.org/10.1007/s10455-024-09968-7","url":null,"abstract":"<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>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"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
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 0.7 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":"https://doi.org/10.1007/s10455-024-09965-w","url":null,"abstract":"<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>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"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 $$mathfrak {sl}_3$ 型线性微分方程
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-08-06 DOI: 10.1007/s10455-024-09964-x
Boris Doubrov, Tohru Morimoto
{"title":"Extrinsic geometry and linear differential equations of $$mathfrak {sl}_3$$ -type","authors":"Boris Doubrov, Tohru Morimoto","doi":"10.1007/s10455-024-09964-x","DOIUrl":"https://doi.org/10.1007/s10455-024-09964-x","url":null,"abstract":"<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>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"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 0.7 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, Bianca Di Blasio, Fulvio Ricci","doi":"10.1007/s10455-024-09963-y","DOIUrl":"https://doi.org/10.1007/s10455-024-09963-y","url":null,"abstract":"<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>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","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":"","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":"https://doi.org/10.1007/s10455-024-09954-z","url":null,"abstract":"","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","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":"","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 0.7 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":"https://doi.org/10.1007/s10455-024-09962-z","url":null,"abstract":"<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>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"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 0.7 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, Riccardo Piovani","doi":"10.1007/s10455-024-09961-0","DOIUrl":"https://doi.org/10.1007/s10455-024-09961-0","url":null,"abstract":"<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. </p>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","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":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Locally conformally Kähler spaces and proper open morphisms 局部保角凯勒空间和适当的开放变形
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-06-13 DOI: 10.1007/s10455-024-09959-8
Ovidiu Preda, Miron Stanciu
{"title":"Locally conformally Kähler spaces and proper open morphisms","authors":"Ovidiu Preda, Miron Stanciu","doi":"10.1007/s10455-024-09959-8","DOIUrl":"https://doi.org/10.1007/s10455-024-09959-8","url":null,"abstract":"<p>In this paper, we prove a stability result for the non-Kähler geometry of locally conformally Kähler (lcK) spaces with singularities. Specifically, we find sufficient conditions under which the image of an lcK space by a holomorphic mapping also admits lcK metrics, thus extending a result by Varouchas about Kähler spaces.</p>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505491","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
Topological degree for Kazdan–Warner equation in the negative case on finite graph 有限图上负情况下卡兹丹-瓦纳方程的拓扑度
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-06-02 DOI: 10.1007/s10455-024-09960-1
Yang Liu, Yunyan Yang
{"title":"Topological degree for Kazdan–Warner equation in the negative case on finite graph","authors":"Yang Liu, Yunyan Yang","doi":"10.1007/s10455-024-09960-1","DOIUrl":"https://doi.org/10.1007/s10455-024-09960-1","url":null,"abstract":"<p>Let <span>(G=left( V,Eright) )</span> be a connected finite graph. We are concerned about the Kazdan–Warner equation in the negative case on <i>G</i>, say </p><span>$$begin{aligned} -Delta u=h_lambda e^{2u}-c, end{aligned}$$</span><p>where <span>(Delta )</span> is the graph Laplacian, <span>(c&lt;0)</span> is a real constant, <span>(h_lambda =h+lambda )</span>, <span>(h:Vrightarrow mathbb {R})</span> is a function satisfying <span>(hle max _{V}h=0)</span> and <span>(hnot equiv 0)</span>, <span>(lambda in mathbb {R})</span>. In this paper, using the method of topological degree, we prove that there exists a critical value <span>(Lambda ^*in (0,-min _{V}h))</span> such that if <span>(lambda in (-infty ,Lambda ^*])</span>, then the above equation has solutions; and that if <span>(lambda in (Lambda ^*,+infty ))</span>, then it has no solution. Specifically, if <span>(lambda in (-infty ,0])</span>, then it has a unique solution; if <span>(lambda in (0,Lambda ^*))</span>, then it has at least two distinct solutions, of which one is a local minimum solution; while if <span>(lambda =Lambda ^*)</span>, it has at least one solution. For the proof of these results, we first calculate the topological degree of a map related to the above equation, and then we utilize the relationship between the topological degree and the critical group of the relevant functional. Our method is essentially different from that of Liu and Yang (Calc. Var. 59 (2020), 164), who obtained similar results by using a method of variation.</p>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141197955","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
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