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Sasaki–Einstein 7-manifolds and Orlik’s conjecture Sasaki-Einstein 7-流形和Orlik猜想
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-11-16 DOI: 10.1007/s10455-023-09930-z
Jaime Cuadros Valle, Joe Lope Vicente
{"title":"Sasaki–Einstein 7-manifolds and Orlik’s conjecture","authors":"Jaime Cuadros Valle,&nbsp;Joe Lope Vicente","doi":"10.1007/s10455-023-09930-z","DOIUrl":"10.1007/s10455-023-09930-z","url":null,"abstract":"<div><p>We study the homology groups of certain 2-connected 7-manifolds admitting quasi-regular Sasaki–Einstein metrics, among them, we found 52 new examples of Sasaki–Einstein rational homology 7-spheres, extending the list given by Boyer et al. (Ann Inst Fourier 52(5):1569–1584, 2002). As a consequence, we exhibit new families of positive Sasakian homotopy 9-spheres given as cyclic branched covers, determine their diffeomorphism types and find out which elements do not admit extremal Sasaki metrics. We also improve previous results given by Boyer (Note Mat 28:63–105, 2008) showing new examples of Sasaki–Einstein 2-connected 7-manifolds homeomorphic to connected sums of <span>(S^3times S^4)</span>. Actually, we show that manifolds of the form <span>(#kleft( S^{3} times S^{4}right) )</span> admit Sasaki–Einstein metrics for 22 different values of <i>k</i>. All these links arise as Thom–Sebastiani sums of chain type singularities and cycle type singularities where Orlik’s conjecture holds due to a recent result by Hertling and Mase (J Algebra Number Theory 16(4):955–1024, 2022).</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796801","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
Berglund–Hübsch transpose rule and Sasakian geometry berglund - h<s:1> bsch转置定则与sasaki几何
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-11-16 DOI: 10.1007/s10455-023-09932-x
Ralph R. Gomez
{"title":"Berglund–Hübsch transpose rule and Sasakian geometry","authors":"Ralph R. Gomez","doi":"10.1007/s10455-023-09932-x","DOIUrl":"10.1007/s10455-023-09932-x","url":null,"abstract":"<div><p>We apply the Berglund–Hübsch transpose rule from BHK mirror symmetry to show that to an <span>(n-1)</span>-dimensional Calabi–Yau orbifold in weighted projective space defined by an invertible polynomial, we can associate four (possibly) distinct Sasaki manifolds of dimension <span>(2n+1)</span> which are <span>(n-1)</span>-connected and admit a metric of positive Ricci curvature. We apply this theorem to show that for a given K3 orbifold, there exist four seven-dimensional Sasakian manifolds of positive Ricci curvature, two of which are actually Sasaki–Einstein.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796802","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: 1
Boundary properties for a Monge-Ampère equation of prescribed affine Gauss curvature 给定仿射高斯曲率的monge - ampantere方程的边界性质
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-11-16 DOI: 10.1007/s10455-023-09933-w
Yadong Wu
{"title":"Boundary properties for a Monge-Ampère equation of prescribed affine Gauss curvature","authors":"Yadong Wu","doi":"10.1007/s10455-023-09933-w","DOIUrl":"10.1007/s10455-023-09933-w","url":null,"abstract":"<div><p>Considering a Monge-Ampère equation with prescribed affine Gauss curvature, we first show the completeness of centroaffine metric on the convex domain and derive a gradient estimate of the convex solution and then give different orders of two eigenvalues of the Hessian with respect to the distance function. We also show that the curvature of level sets of the convex solution is uniformly bounded, and show that there exist a class of Euclidean-complete hyperbolic surfaces with prescribed affine Gauss curvature and with bounded affine principal curvatures.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796803","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
The metric structure of compact rank-one ECS manifolds 紧致1阶ECS流形的度量结构
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-10-26 DOI: 10.1007/s10455-023-09929-6
Andrzej Derdzinski, Ivo Terek
{"title":"The metric structure of compact rank-one ECS manifolds","authors":"Andrzej Derdzinski,&nbsp;Ivo Terek","doi":"10.1007/s10455-023-09929-6","DOIUrl":"10.1007/s10455-023-09929-6","url":null,"abstract":"<div><p>Pseudo-Riemannian manifolds with nonzero parallel Weyl tensor which are not locally symmetric are known as ECS manifolds. Every ECS manifold carries a distinguished null parallel distribution <span>(mathcal {D})</span>, the rank <span>(din {1,2})</span> of which is referred to as the rank of the manifold itself. Under a natural genericity assumption on the Weyl tensor, we fully describe the universal coverings of compact rank-one ECS manifolds. We then show that any generic compact rank-one ECS manifold must be <i>translational</i>, in the sense that the holonomy group of the natural flat connection induced on <span>(mathcal {D})</span> is either trivial or isomorphic to <span>({mathbb {Z}}_2)</span>. We also prove that all four-dimensional rank-one ECS manifolds are noncompact, this time without having to assume genericity, as it is always the case in dimension four.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09929-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797739","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: 3
Harmonic flow of geometric structures 几何结构的谐波流动
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-10-17 DOI: 10.1007/s10455-023-09928-7
Eric Loubeau, Henrique N. Sá Earp
{"title":"Harmonic flow of geometric structures","authors":"Eric Loubeau,&nbsp;Henrique N. Sá Earp","doi":"10.1007/s10455-023-09928-7","DOIUrl":"10.1007/s10455-023-09928-7","url":null,"abstract":"<div><p>We give a twistorial interpretation of geometric structures on a Riemannian manifold, as sections of homogeneous fibre bundles, following an original insight by Wood (Differ Geom Appl 19:193–210, 2003). The natural Dirichlet energy induces an abstract harmonicity condition, which gives rise to a geometric gradient flow. We establish a number of analytic properties for this flow, such as uniqueness, smoothness, short-time existence, and some sufficient conditions for long-time existence. This description potentially subsumes a large class of geometric PDE problems from different contexts. As applications, we recover and unify a number of results in the literature: for the isometric flow of <span>(text {G}_2)</span>-structures, by Grigorian (Adv Math 308:142–207, 2017; Calculas Variat Partial Differ Equ 58:157, 2019), Bagaglini (J Geom Anal, 2009), and Dwivedi-Gianniotis-Karigiannis (J Geom Anal 31(2):1855-1933, 2021); and for harmonic almost complex structures, by He (Energy minimizing harmonic almost complex structures, 2019) and He-Li (Trans Am Math Soc 374(9):6179–6199, 2021). Our theory also establishes original properties regarding harmonic flows of parallelisms and almost contact structures.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09928-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50491887","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: 14
On the index of a free-boundary minimal surface in Riemannian Schwarzschild-AdS 关于Riemann-Schwarzschild AdS中自由边界极小曲面的指数
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-10-04 DOI: 10.1007/s10455-023-09925-w
Justin Corvino, Elene Karangozishvili, Deniz Ozbay
{"title":"On the index of a free-boundary minimal surface in Riemannian Schwarzschild-AdS","authors":"Justin Corvino,&nbsp;Elene Karangozishvili,&nbsp;Deniz Ozbay","doi":"10.1007/s10455-023-09925-w","DOIUrl":"10.1007/s10455-023-09925-w","url":null,"abstract":"<div><p>We consider the index of a certain non-compact free-boundary minimal surface with boundary on the rotationally symmetric minimal sphere in the Schwarzschild-AdS geometry with <span>(m&gt;0)</span>. As in the Schwarzschild case, we show that in dimensions <span>(nge 4)</span>, the surface is stable, whereas in dimension three, the stability depends on the value of the mass <span>(m&gt;0)</span> and the cosmological constant <span>(Lambda &lt;0)</span> via the parameter <span>(mu :=msqrt{-Lambda /3})</span>. We show that while for <span>(mu ge tfrac{5}{27})</span> the surface is stable, there exist positive numbers <span>(mu _0)</span> and <span>(mu _1)</span>, with <span>(mu _1&lt;tfrac{5}{27})</span>, such that for <span>(0&lt;mu &lt;mu _0)</span>, the surface is unstable, while for all <span>(mu ge mu _1)</span>, the index is at most one.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09925-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50450580","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
Solution to the n-bubble problem on (mathbb {R}^1) with log-concave density 具有对数凹密度的（mathbb｛R｝^1）上n气泡问题的解
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-09-28 DOI: 10.1007/s10455-023-09927-8
John Ross
{"title":"Solution to the n-bubble problem on (mathbb {R}^1) with log-concave density","authors":"John Ross","doi":"10.1007/s10455-023-09927-8","DOIUrl":"10.1007/s10455-023-09927-8","url":null,"abstract":"<div><p>We study the <i>n</i>-bubble problem on <span>(mathbb {R}^1)</span> with a prescribed density function <i>f</i> that is even, radially increasing, and satisfies a log-concavity requirement. Under these conditions, we find that isoperimetric solutions can be identified for an arbitrary number of regions, and that these solutions have a well-understood and regular structure. This generalizes recent work done on the density function <span>(|x |^p)</span> and stands in contrast to log-convex density functions which are known to have no such regular structure.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09927-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50522011","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
Compactness of harmonic maps of surfaces with regular nodes 具有正则节点的曲面调和映射的紧性
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-09-25 DOI: 10.1007/s10455-023-09926-9
Woongbae Park
{"title":"Compactness of harmonic maps of surfaces with regular nodes","authors":"Woongbae Park","doi":"10.1007/s10455-023-09926-9","DOIUrl":"10.1007/s10455-023-09926-9","url":null,"abstract":"<div><p>In this paper, we formulate and prove a general compactness theorem for harmonic maps of Riemann surfaces using Deligne–Mumford moduli space and families of curves. The main theorem shows that given a sequence of harmonic maps over a sequence of complex curves, there is a family of curves and a subsequence such that both the domains and the maps converge with the singular set consisting of only “non-regular” nodes. This provides a sufficient condition for a neck having zero energy and zero length. As a corollary, the following known fact can be proved: If all domains are diffeomorphic to <span>(S^2)</span>, both energy identity and zero distance bubbling hold.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50514864","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
Dirichlet problem for harmonic maps from strongly rectifiable spaces into regular balls in ({text {CAT}}(1)) spaces （1）空间中从强可直空间到正则球的调和映射的Dirichlet问题
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-09-16 DOI: 10.1007/s10455-023-09924-x
Yohei Sakurai
{"title":"Dirichlet problem for harmonic maps from strongly rectifiable spaces into regular balls in ({text {CAT}}(1)) spaces","authors":"Yohei Sakurai","doi":"10.1007/s10455-023-09924-x","DOIUrl":"10.1007/s10455-023-09924-x","url":null,"abstract":"<div><p>In this note, we study the Dirichlet problem for harmonic maps from strongly rectifiable spaces into regular balls in <span>({text {CAT}}(1))</span> space. Under the setting, we prove that the Korevaar–Schoen energy admits a unique minimizer.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50488485","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
Modified conformal extensions 改进的共形扩展
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-09-13 DOI: 10.1007/s10455-023-09918-9
Matthias Hammerl, Katja Sagerschnig, Josef Šilhan, Vojtěch Žádník
{"title":"Modified conformal extensions","authors":"Matthias Hammerl,&nbsp;Katja Sagerschnig,&nbsp;Josef Šilhan,&nbsp;Vojtěch Žádník","doi":"10.1007/s10455-023-09918-9","DOIUrl":"10.1007/s10455-023-09918-9","url":null,"abstract":"<div><p>We present a geometric construction and characterization of 2<i>n</i>-dimensional split-signature conformal structures endowed with a twistor spinor with integrable kernel. The construction is regarded as a modification of the conformal Patterson–Walker metric construction for <i>n</i>-dimensional projective manifolds. The characterization is presented in terms of the twistor spinor and an integrability condition on the conformal Weyl curvature. We further derive a complete description of Einstein metrics and infinitesimal conformal symmetries in terms of suitable projective data. Finally, we obtain an explicit geometrically constructed Fefferman–Graham ambient metric and show the vanishing of the <i>Q</i>-curvature.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09918-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50479147","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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