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Annals of Global Analysis and Geometry最新文献

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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
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 0.6 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,&nbsp;Miron Stanciu","doi":"10.1007/s10455-024-09959-8","DOIUrl":"10.1007/s10455-024-09959-8","url":null,"abstract":"<div><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></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"66 1","pages":""},"PeriodicalIF":0.6,"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 0.6 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,&nbsp;Yunyan Yang","doi":"10.1007/s10455-024-09960-1","DOIUrl":"10.1007/s10455-024-09960-1","url":null,"abstract":"<div><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><div><div><span>$$begin{aligned} -Delta u=h_lambda e^{2u}-c, end{aligned}$$</span></div></div><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></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 4","pages":""},"PeriodicalIF":0.6,"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
Self-dual almost-Kähler four-manifolds 自偶几乎-凯勒四漫游
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-05-19 DOI: 10.1007/s10455-024-09958-9
Inyoung Kim
{"title":"Self-dual almost-Kähler four-manifolds","authors":"Inyoung Kim","doi":"10.1007/s10455-024-09958-9","DOIUrl":"10.1007/s10455-024-09958-9","url":null,"abstract":"<div><p>We classify compact self-dual almost-Kähler four-manifolds of positive type and zero type. In particular, using LeBrun’s result, we show that any self-dual almost-Kähler metric on a manifold which is diffeomorphic to <span>({{mathbb {C}}}{{mathbb {P}}}_{2})</span> is the Fubini-Study metric on <span>({{mathbb {C}}}{{mathbb {P}}}_{2})</span> up to rescaling. In case of negative type, we classify compact self-dual almost-Kähler four-manifolds with <i>J</i>-invariant ricci tensor.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153875","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
Contact foliations and generalised Weinstein conjectures 接触叶面和广义韦恩斯坦猜想
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-05-09 DOI: 10.1007/s10455-024-09957-w
Douglas Finamore
{"title":"Contact foliations and generalised Weinstein conjectures","authors":"Douglas Finamore","doi":"10.1007/s10455-024-09957-w","DOIUrl":"10.1007/s10455-024-09957-w","url":null,"abstract":"<div><p>We consider contact foliations: objects which generalise to higher dimensions the flow of the Reeb vector field on contact manifolds. We list several properties of such foliations and propose two conjectures about the topological types of their leaves, both of which coincide with the classical Weinstein conjecture in the case of contact flows. We give positive partial results for our conjectures in particular cases—when the holonomy of the contact foliation preserves a Riemannian metric, for instance—extending already established results in the field of Contact Dynamics.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140927383","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
Fill-ins with scalar curvature lower bounds and applications to positive mass theorems 标量曲率下限的填充和正质量定理的应用
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-05-06 DOI: 10.1007/s10455-024-09956-x
Stephen McCormick
{"title":"Fill-ins with scalar curvature lower bounds and applications to positive mass theorems","authors":"Stephen McCormick","doi":"10.1007/s10455-024-09956-x","DOIUrl":"10.1007/s10455-024-09956-x","url":null,"abstract":"<div><p>Given a constant <i>C</i> and a smooth closed <span>((n-1))</span>-dimensional Riemannian manifold <span>((Sigma , g))</span> equipped with a positive function <i>H</i>, a natural question to ask is whether this manifold can be realised as the boundary of a smooth <i>n</i>-dimensional Riemannian manifold with scalar curvature bounded below by <i>C</i> and boundary mean curvature <i>H</i>. That is, does there exist a <i>fill-in</i> of <span>((Sigma ,g,H))</span> with scalar curvature bounded below by <i>C</i>? We use variations of an argument due to Miao and the author (Int Math Res Not 7:2019, 2019) to explicitly construct fill-ins with different scalar curvature lower bounds, where we permit the fill-in to contain another boundary component provided it is a minimal surface. Our main focus is to illustrate the applications of such fill-ins to geometric inequalities in the context of general relativity. By filling in a manifold beyond a boundary, one is able to obtain lower bounds on the mass in terms of the boundary geometry through positive mass theorems and Penrose inequalities. We consider fill-ins with both positive and negative scalar curvature lower bounds, which from the perspective of general relativity corresponds to the sign of the cosmological constant, as well as a fill-in suitable for the inclusion of electric charge.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-024-09956-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889039","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
Well-posedness of nonlinear flows on manifolds of bounded geometry 有界几何流形上非线性流的好求性
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-05-06 DOI: 10.1007/s10455-023-09940-x
Eric Bahuaud, Christine Guenther, James Isenberg, Rafe Mazzeo
{"title":"Well-posedness of nonlinear flows on manifolds of bounded geometry","authors":"Eric Bahuaud,&nbsp;Christine Guenther,&nbsp;James Isenberg,&nbsp;Rafe Mazzeo","doi":"10.1007/s10455-023-09940-x","DOIUrl":"10.1007/s10455-023-09940-x","url":null,"abstract":"<div><p>We present straightforward conditions which ensure that a strongly elliptic linear operator <i>L</i> generates an analytic semigroup on Hölder spaces on an arbitrary complete manifold of bounded geometry. This is done by establishing the equivalent property that <i>L</i> is ‘sectorial,’ a condition that specifies the decay of the resolvent <span>((lambda I - L)^{-1})</span> as <span>(lambda )</span> diverges from the Hölder spectrum of <i>L</i>. A key step is that we prove existence of this resolvent if <span>(lambda )</span> is sufficiently large using a geometric microlocal version of the semiclassical pseudodifferential calculus. The properties of <i>L</i> and <span>(e^{-tL})</span> we obtain can then be used to prove well-posedness of a wide class of nonlinear flows. We illustrate this by proving well-posedness on Hölder spaces of the flow associated with the ambient obstruction tensor on complete manifolds of bounded geometry. This new result for a higher-order flow on a noncompact manifold exhibits the broader applicability of our technique.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889028","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
Variation formulae for the volume of coassociative submanifolds 共轭子实体体积的变化公式
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2024-04-29 DOI: 10.1007/s10455-024-09955-y
Tommaso Pacini, Alberto Raffero
{"title":"Variation formulae for the volume of coassociative submanifolds","authors":"Tommaso Pacini,&nbsp;Alberto Raffero","doi":"10.1007/s10455-024-09955-y","DOIUrl":"10.1007/s10455-024-09955-y","url":null,"abstract":"<div><p>We prove new variation formulae for the volume of coassociative submanifolds, expressed in terms of <span>(G_2)</span> data. These formulae highlight the role of the ambient torsion and Ricci curvature. As a special case, we obtain a second variation formula for variations within the moduli space of coassociative submanifolds. These results apply, for example, to coassociative fibrations. We illustrate our formulae with several examples, both homogeneous and non.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140810005","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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