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Annals of Global Analysis and Geometry最新文献

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On the existence and properties of solutions of the generalized Jang equation with respect to asymptotically anti-de Sitter initial data 关于渐近反de Sitter初始数据的广义Jang方程解的存在性和性质
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-08-04 DOI: 10.1007/s10455-025-10013-4
Benjamin Meco
{"title":"On the existence and properties of solutions of the generalized Jang equation with respect to asymptotically anti-de Sitter initial data","authors":"Benjamin Meco","doi":"10.1007/s10455-025-10013-4","DOIUrl":"10.1007/s10455-025-10013-4","url":null,"abstract":"<div><p>We provide a rigorous analysis of the generalized Jang equation in the asymptotically anti-de Sitter setting modelled on constant time slices of anti-de Sitter spacetimes in dimensions <span>(3le n le 7)</span> for a very general class of asymptotics. Potential applications to spacetime positive mass theorems for asymptotically anti-de Sitter initial data sets are discussed.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"68 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-025-10013-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145142353","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
Analytic K-semistability and local wall-crossing 解析k -半稳定性与局部过壁
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-07-15 DOI: 10.1007/s10455-025-10011-6
Lars Martin Sektnan, Carl Tipler
{"title":"Analytic K-semistability and local wall-crossing","authors":"Lars Martin Sektnan,&nbsp;Carl Tipler","doi":"10.1007/s10455-025-10011-6","DOIUrl":"10.1007/s10455-025-10011-6","url":null,"abstract":"<div><p>For a small polarised deformation of a constant scalar curvature Kähler manifold, under some cohomological vanishing conditions, we prove that <i>K</i>-polystability along nearby polarisations implies the existence of a constant scalar curvature Kähler metric. In this setting, we reduce <i>K</i>-polystability to the computation of the classical Futaki invariant on the cscK degeneration. Our result holds on specific families and provides local wall-crossing phenomena for the moduli of cscK manifolds when the polarisation varies.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"68 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-025-10011-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143771","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
Exotic almost complex circle actions on 6-manifolds 6流形上奇异的几乎复杂的圆作用
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-07-14 DOI: 10.1007/s10455-025-09988-x
Panagiotis Konstantis, Nicholas Lindsay
{"title":"Exotic almost complex circle actions on 6-manifolds","authors":"Panagiotis Konstantis,&nbsp;Nicholas Lindsay","doi":"10.1007/s10455-025-09988-x","DOIUrl":"10.1007/s10455-025-09988-x","url":null,"abstract":"<div><p>Jang has proven a remarkable classification of 6-dimensional manifolds having an almost complex circle action with 4 fixed points. Jang classifies the weights and associated multigraph into six cases, leaving the existence of connected manifolds fitting into two of the cases unknown. We show that one of the unknown cases may be constructed by a surgery construction of Kustarev, and the underlying manifold is diffeomorphic to <span>(S^4 times S^2)</span>. We show that the action is not equivariantly diffeomorphic to a linear one, thus giving an exotic <span>(S^1)</span>-action of on a product of spheres that preserves an almost complex structure. We also prove a uniqueness statement for the almost complex structures produced by Kustarev’s construction and prove some topological applications of Jang’s classification.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"68 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-025-09988-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143926","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
Transversality for perturbed special lagrangian submanifolds 摄动特殊拉格朗日子流形的横向性
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-07-12 DOI: 10.1007/s10455-025-10006-3
Emily Autumn Windes
{"title":"Transversality for perturbed special lagrangian submanifolds","authors":"Emily Autumn Windes","doi":"10.1007/s10455-025-10006-3","DOIUrl":"10.1007/s10455-025-10006-3","url":null,"abstract":"<div><p>We prove a transversality theorem for the moduli space of perturbed special Lagrangian submanifolds in a 6-manifold equipped with a generalization of a Calabi–Yau structure. These perturbed special Lagrangian submanifolds arise as solutions to an infinite-dimensional Lagrange multipliers problem which is part of a proposal for counting special Lagrangians outlined by Donaldson and Segal in [9]. More specifically, we prove that this moduli space is generically a set of isolated points.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"68 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-025-10006-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143138","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
Diameter and focal radius of submanifolds 子流形的直径和焦半径
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-07-02 DOI: 10.1007/s10455-025-10010-7
Ricardo A. E. Mendes
{"title":"Diameter and focal radius of submanifolds","authors":"Ricardo A. E. Mendes","doi":"10.1007/s10455-025-10010-7","DOIUrl":"10.1007/s10455-025-10010-7","url":null,"abstract":"<div><p>In this note, we give a characterization of immersed submanifolds of simply-connected space forms for which the quotient of the extrinsic diameter by the focal radius achieves the minimum possible value of 2. They are essentially round spheres, or the “Veronese” embeddings of projective spaces. The proof combines the classification of submanifolds with planar geodesics due to K. Sakamoto with a version of A. Schur’s Bow Lemma for space curves. Open problems and the relation to recent work by M. Gromov and A. Petrunin are discussed.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"68 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145141963","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 the variation of r-mean curvature functionals and application to the (L^2)-norm of the traceless second fundamental form r-均值曲率泛函的变分及其在无迹第二基本形式(L^2) -范数中的应用
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-07-02 DOI: 10.1007/s10455-025-10009-0
Thiago Pires, Walcy Santos
{"title":"On the variation of r-mean curvature functionals and application to the (L^2)-norm of the traceless second fundamental form","authors":"Thiago Pires,&nbsp;Walcy Santos","doi":"10.1007/s10455-025-10009-0","DOIUrl":"10.1007/s10455-025-10009-0","url":null,"abstract":"<div><p>Functionals involving surface curvatures are objects with applications in physics, mathematics, and related areas. It is then natural to study the minimizers of these functionals, as well as the stability of its critical points. In this paper, we begin by examining a general functional on <i>n</i>-dimensional hypersurfaces, which depends on the 1-mean curvature and the 2-mean curvature. We compute its first variation formula, obtaining the Euler-Lagrange equation that characterizes critical points. As a consequence, we also obtain the Euler-Lagrange equation for hypersurfaces immersed in Einstein manifolds as well as in manifolds with constant sectional curvature. In the case where the ambient space is a manifold with constant sectional curvature, we also compute the second variation, obtaining a stability criterion for these points in terms of geometric invariants that depend solely on the first and second fundamental forms. These results generalize those obtained in [7]. To demonstrate the applicability of the results, we studied the functional given by the <span>(L^2)</span>-norm of the traceless second fundamental form. From a geometric perspective, <span>(Phi )</span> is a functional that measures how much <i>M</i> deviates from being totally umbilical, that is, from having equal principal curvatures at every point. We investigated the Euler-Lagrange equation and checked the stability of some known critical points.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"68 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145141863","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
Ricci pinched compact submanifolds in spheres 球中的Ricci捏紧紧子流形
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-06-30 DOI: 10.1007/s10455-025-10007-2
Marcos Dajczer, Theodoros Vlachos
{"title":"Ricci pinched compact submanifolds in spheres","authors":"Marcos Dajczer,&nbsp;Theodoros Vlachos","doi":"10.1007/s10455-025-10007-2","DOIUrl":"10.1007/s10455-025-10007-2","url":null,"abstract":"<div><p>We investigate the topology of the compact submanifolds in round spheres that satisfy a lower bound on the Ricci curvature depending only on the length of the mean curvature vector of the immersion. Just in special cases, the limited strength of the assumption allows some strong additional information on the extrinsic geometry of the submanifold.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"68 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-025-10007-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171643","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
What Uniqueness for the Holst-Nagy-Tsogtgerel–Maxwell Solutions to the Einstein Conformal Constraint Equations? 爱因斯坦共形约束方程的Holst-Nagy-Tsogtgerel-Maxwell解的唯一性？
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-06-25 DOI: 10.1007/s10455-025-10000-9
Romain Gicquaud
{"title":"What Uniqueness for the Holst-Nagy-Tsogtgerel–Maxwell Solutions to the Einstein Conformal Constraint Equations?","authors":"Romain Gicquaud","doi":"10.1007/s10455-025-10000-9","DOIUrl":"10.1007/s10455-025-10000-9","url":null,"abstract":"<div><p>This paper addresses the issue of uniqueness of solutions in the conformal method for solving the constraint equations in general relativity with arbitrary mean curvature as developed initially by Holst, Nagy, Tsogtegerel and Maxwell. We show that, under a technical assumption, the solution they construct is unique amongst those having volume below a certain threshold.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"68 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169818","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
Small eigenvalues of the Hodge-Laplacian with sectional curvature bounded below 截面曲率有界的Hodge-Laplacian的小特征值
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-06-23 DOI: 10.1007/s10455-025-10005-4
Colette Anné, Junya Takahashi
{"title":"Small eigenvalues of the Hodge-Laplacian with sectional curvature bounded below","authors":"Colette Anné,&nbsp;Junya Takahashi","doi":"10.1007/s10455-025-10005-4","DOIUrl":"10.1007/s10455-025-10005-4","url":null,"abstract":"<div><p>For each degree <i>p</i> and each natural number <span>(k ge 1)</span>, we construct a one-parameter family of Riemannian metrics on any oriented closed manifold with volume one and the sectional curvature bounded below such that the <i>k</i>-th positive eigenvalue of the Hodge-Laplacian acting on differential <i>p</i>-forms converges to zero. This result imposes a constraint on the sectional curvature for our previous result in [1].</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"68 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168364","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
Invariant Monge–Ampère equations on contactified para–Kähler manifolds 接触para-Kähler流形上的不变monge - ampante方程
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-05-29 DOI: 10.1007/s10455-025-09999-8
Dmitri Alekseevsky, Gianni Manno, Giovanni Moreno
{"title":"Invariant Monge–Ampère equations on contactified para–Kähler manifolds","authors":"Dmitri Alekseevsky,&nbsp;Gianni Manno,&nbsp;Giovanni Moreno","doi":"10.1007/s10455-025-09999-8","DOIUrl":"10.1007/s10455-025-09999-8","url":null,"abstract":"<div><p>We develop a method for describing invariant PDEs of Monge–Ampère type in the sense of Lychagin and Morimoto (MAE) on a homogeneous contact manifold <i>N</i> of a semisimple Lie group <i>G</i>, which is the <i>contactification</i> of the homogeneous symplectic manifold <span>(M = G/H = textrm{Ad}_G Z subset mathfrak {g})</span>, where <i>M</i> is the adjoint orbit of a splittable closed element <i>Z</i> of the Lie algebra <span>(mathfrak {g}= {{,textrm{Lie},}}(G))</span>. The method is then applied to a ten-dimensional semisimple orbit <i>M</i> of the exceptional Lie group <span>(textsf{G}_2)</span> and a complete list of mutually non-equivalent MAEs on <i>N</i> is obtained.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-025-09999-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171389","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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