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Annals of Global Analysis and Geometry最新文献

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Compact surfaces with boundary with prescribed mean curvature depending on the Gauss map 根据高斯映射，具有指定平均曲率边界的紧致曲面
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-07-03 DOI: 10.1007/s10455-023-09910-3
Antonio Bueno, Rafael López
{"title":"Compact surfaces with boundary with prescribed mean curvature depending on the Gauss map","authors":"Antonio Bueno,&nbsp;Rafael López","doi":"10.1007/s10455-023-09910-3","DOIUrl":"10.1007/s10455-023-09910-3","url":null,"abstract":"<div><p>Given a <span>(C^1)</span> function <span>(mathcal {H})</span> defined in the unit sphere <span>(mathbb {S}^2)</span>, an <span>(mathcal {H})</span>-surface <i>M</i> is a surface in the Euclidean space <span>(mathbb {R}^3)</span> whose mean curvature <span>(H_M)</span> satisfies <span>(H_M(p)=mathcal {H}(N_p))</span>, <span>(pin M)</span>, where <i>N</i> is the Gauss map of <i>M</i>. Given a closed simple curve <span>(Gamma subset mathbb {R}^3)</span> and a function <span>(mathcal {H})</span>, in this paper we investigate the geometry of compact <span>(mathcal {H})</span>-surfaces spanning <span>(Gamma )</span> in terms of <span>(Gamma )</span>. Under mild assumptions on <span>(mathcal {H})</span>, we prove non-existence of closed <span>(mathcal {H})</span>-surfaces, in contrast with the classical case of constant mean curvature. We give conditions on <span>(mathcal {H})</span> that ensure that if <span>(Gamma )</span> is a circle, then <i>M</i> is a rotational surface. We also establish the existence of estimates of the area of <span>(mathcal {H})</span>-surfaces in terms of the height of the surface.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43478109","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
Anti-quasi-Sasakian manifolds Anti-quasi-Sasakian manifolds
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-06-26 DOI: 10.1007/s10455-023-09907-y
D. Di Pinto, G. Dileo
{"title":"Anti-quasi-Sasakian manifolds","authors":"D. Di Pinto,&nbsp;G. Dileo","doi":"10.1007/s10455-023-09907-y","DOIUrl":"10.1007/s10455-023-09907-y","url":null,"abstract":"<div><p>We introduce and study a special class of almost contact metric manifolds, which we call anti-quasi-Sasakian (aqS). Among the class of transversely Kähler almost contact metric manifolds <span>((M,varphi , xi ,eta ,g))</span>, quasi-Sasakian and anti-quasi-Sasakian manifolds are characterized, respectively, by the <span>(varphi )</span>-invariance and the <span>(varphi )</span>-anti-invariance of the 2-form <span>(textrm{d}eta )</span>. A Boothby–Wang type theorem allows to obtain aqS structures on principal circle bundles over Kähler manifolds endowed with a closed (2, 0)-form. We characterize aqS manifolds with constant <span>(xi )</span>-sectional curvature equal to 1: they admit an <span>(Sp(n)times 1)</span>-reduction of the frame bundle such that the manifold is transversely hyperkähler, carrying a second aqS structure and a null Sasakian <span>(eta )</span>-Einstein structure. We show that aqS manifolds with constant sectional curvature are necessarily flat and cokähler. Finally, by using a metric connection with torsion, we provide a sufficient condition for an aqS manifold to be locally decomposable as the Riemannian product of a Kähler manifold and an aqS manifold with structure of maximal rank. Under the same hypothesis, (<i>M</i>, <i>g</i>) cannot be locally symmetric.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09907-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45705860","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: 2
Levi-flat CR structures on compact Lie groups 紧李群上的列维平面CR结构
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-06-21 DOI: 10.1007/s10455-023-09909-w
Howard Jacobowitz, Max Reinhold Jahnke
{"title":"Levi-flat CR structures on compact Lie groups","authors":"Howard Jacobowitz,&nbsp;Max Reinhold Jahnke","doi":"10.1007/s10455-023-09909-w","DOIUrl":"10.1007/s10455-023-09909-w","url":null,"abstract":"<div><p>Pittie (Proc Indian Acad Sci Math Sci 98:117-152, 1988) proved that the Dolbeault cohomology of all left-invariant complex structures on compact Lie groups can be computed by looking at the Dolbeault cohomology induced on a conveniently chosen maximal torus. We generalized Pittie’s result to left-invariant Levi-flat CR structures of maximal rank on compact Lie groups. The main tools we used was a version of the Leray–Hirsch theorem for CR principal bundles and the algebraic classification of left-invariant CR structures of maximal rank on compact Lie groups (Charbonnel and Khalgui in J Lie Theory 14:165-198, 2004) .</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09909-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42624146","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: 1
Integral decompositions of varifolds 变分的积分分解
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-06-21 DOI: 10.1007/s10455-023-09908-x
Hsin-Chuang Chou
{"title":"Integral decompositions of varifolds","authors":"Hsin-Chuang Chou","doi":"10.1007/s10455-023-09908-x","DOIUrl":"10.1007/s10455-023-09908-x","url":null,"abstract":"<div><p>This paper introduces a notion of decompositions of integral varifolds into countably many integral varifolds, and the existence of such decomposition of integral varifolds whose first variation is representable by integration is established. However, the decompositions may fail to be unique. Furthermore, this result can be generalized by replacing the class of integral varifolds with some classes of rectifiable varifolds whose density is uniformly bounded from below; for these classes, we also prove a general version of the compactness theorem for integral varifolds.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42138858","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: 2
Extra-twisted connected sum (G_2)-manifolds 超扭连通和（G_2）-流形
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-06-12 DOI: 10.1007/s10455-023-09893-1
Johannes Nordström
{"title":"Extra-twisted connected sum (G_2)-manifolds","authors":"Johannes Nordström","doi":"10.1007/s10455-023-09893-1","DOIUrl":"10.1007/s10455-023-09893-1","url":null,"abstract":"<div><p>We present a construction of closed 7-manifolds of holonomy <span>(G_2)</span>, which generalises Kovalev’s twisted connected sums by taking quotients of the pieces in the construction before gluing. This makes it possible to realise a wider range of topological types, and Crowley, Goette and the author use this to exhibit examples of closed 7-manifolds with disconnected moduli space of holonomy <span>(G_2)</span> metrics.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09893-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50475153","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: 5
Extra-twisted connected sum G2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$G_2$$end{document}-manifolds Extra-twisted connected sum G2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$G_2$$end{document}-manifolds
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-06-12 DOI: 10.1007/s10455-023-09893-1
Johannes Nordström
{"title":"Extra-twisted connected sum G2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$G_2$$end{document}-manifolds","authors":"Johannes Nordström","doi":"10.1007/s10455-023-09893-1","DOIUrl":"https://doi.org/10.1007/s10455-023-09893-1","url":null,"abstract":"","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52192381","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
Existence results for a super Toda system 超级Toda系统的存在性结果
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-06-07 DOI: 10.1007/s10455-023-09899-9
Aleks Jevnikar, Ruijun Wu
{"title":"Existence results for a super Toda system","authors":"Aleks Jevnikar,&nbsp;Ruijun Wu","doi":"10.1007/s10455-023-09899-9","DOIUrl":"10.1007/s10455-023-09899-9","url":null,"abstract":"<div><p>We solve a super Toda system on a closed Riemann surface of genus <span>(gamma &gt;1)</span> and with some particular spin structures. This generalizes the min–max methods and results for super Liouville equations and gives new existence results for super Toda systems.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09899-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44027650","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
Homogeneous Einstein metrics and butterflies 齐次爱因斯坦度量与蝴蝶
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-06-02 DOI: 10.1007/s10455-023-09905-0
Christoph Böhm, Megan M. Kerr
{"title":"Homogeneous Einstein metrics and butterflies","authors":"Christoph Böhm,&nbsp;Megan M. Kerr","doi":"10.1007/s10455-023-09905-0","DOIUrl":"10.1007/s10455-023-09905-0","url":null,"abstract":"<div><p>In 2012, M. M. Graev associated to a compact homogeneous space <i>G</i>/<i>H</i> a nerve <span>({text {X}}_{G/H})</span>, whose non-contractibility implies the existence of a <i>G</i>-invariant Einstein metric on <i>G</i>/<i>H</i>. The nerve <span>({text {X}}_{G/H})</span> is a compact, semi-algebraic set, defined purely Lie theoretically by intermediate subgroups. In this paper we present a detailed description of the work of Graev and the curvature estimates given by Böhm in 2004.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42812695","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: 3
Sobolev inequalities and convergence for Riemannian metrics and distance functions 黎曼度量和距离函数的Sobolev不等式和收敛性
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-06-01 DOI: 10.1007/s10455-023-09906-z
B. Allen, E. Bryden
{"title":"Sobolev inequalities and convergence for Riemannian metrics and distance functions","authors":"B. Allen,&nbsp;E. Bryden","doi":"10.1007/s10455-023-09906-z","DOIUrl":"10.1007/s10455-023-09906-z","url":null,"abstract":"<div><p>If one thinks of a Riemannian metric, <span>(g_1)</span>, analogously as the gradient of the corresponding distance function, <span>(d_1)</span>, with respect to a background Riemannian metric, <span>(g_0)</span>, then a natural question arises as to whether a corresponding theory of Sobolev inequalities exists between the Riemannian metric and its distance function. In this paper, we study the sub-critical case <span>(p &lt; frac{m}{2})</span> where we show a Sobolev inequality exists between a Riemannian metric and its distance function. In particular, we show that an <span>(L^{frac{p}{2}})</span> bound on a Riemannian metric implies an <span>(L^q)</span> bound on its corresponding distance function. We then use this result to state a convergence theorem and show how this theorem can be useful to prove geometric stability results by proving a version of Gromov’s conjecture for tori with almost non-negative scalar curvature in the conformal case. Examples are given to show that the hypotheses of the main theorems are necessary.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43867965","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: 2
On non-compact gradient solitons 关于非紧化梯度孤子
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-05-24 DOI: 10.1007/s10455-023-09904-1
Antonio W. Cunha, Erin Griffin
{"title":"On non-compact gradient solitons","authors":"Antonio W. Cunha,&nbsp;Erin Griffin","doi":"10.1007/s10455-023-09904-1","DOIUrl":"10.1007/s10455-023-09904-1","url":null,"abstract":"<div><p>In this paper, we extend existing results for generalized solitons, called <i>q</i>-solitons, to the complete case by considering non-compact solitons. By placing regularity conditions on the vector field <i>X</i> and curvature conditions on <i>M</i>, we are able to use the chosen properties of the tensor <i>q</i> to see that such non-compact <i>q</i>-solitons are stationary and <i>q</i>-flat. We conclude by applying our results to the examples of ambient obstruction solitons, Cotton solitons, and Bach solitons to demonstrate the utility of these general theorems for various flows.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42518816","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
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