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Generalized Bernstein Theorem for stable minimal plateau surfaces 稳定极小平台曲面的广义Bernstein定理
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-05-24 DOI: 10.1007/s10455-025-10002-7
Gaoming Wang
{"title":"Generalized Bernstein Theorem for stable minimal plateau surfaces","authors":"Gaoming Wang","doi":"10.1007/s10455-025-10002-7","DOIUrl":"10.1007/s10455-025-10002-7","url":null,"abstract":"<div><p>In this paper, we consider a Generalized Bernstein Theorem for a type of generalized minimal surfaces, namely minimal Plateau surfaces. We show that if a complete orientable minimal Plateau surface is stable and has quadratic area growth in <span>(mathbb {R}^3 )</span>, then it must be flat.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144125536","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
G2-instantons on the ALC members of the (mathbb {B}_7) family 在(mathbb {B}_7)家族的ALC成员的G2-instantons
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-05-23 DOI: 10.1007/s10455-025-10003-6
Jakob Stein, Matt Turner
{"title":"G2-instantons on the ALC members of the (mathbb {B}_7) family","authors":"Jakob Stein,&nbsp;Matt Turner","doi":"10.1007/s10455-025-10003-6","DOIUrl":"10.1007/s10455-025-10003-6","url":null,"abstract":"<div><p>Using co-homogeneity one symmetries, we construct a two-parameter family of non-abelian <span>(G_2)</span>-instantons on every member of the asymptotically locally conical <span>(mathbb {B}_7)</span>-family of <span>(G_2)</span>-metrics on <span>(S^3 times mathbb {R}^4 )</span>, and classify the resulting solutions. These solutions can be described as perturbations of a one-parameter family of abelian instantons, arising from the Killing vector-field generating the asymptotic circle fibre. Generically, these perturbations decay exponentially to the model, but we find a one-parameter family of instantons with polynomial decay. Moreover, we relate the two-parameter family to a lift of an explicit two-parameter family of anti-self-dual instantons on Taub-NUT <span>(mathbb {R}^4)</span>, fibred over <span>(S^3)</span> in an adiabatic limit.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144125580","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
Dimension reduction for positively curved steady solitons 正弯曲稳定孤子的降维
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-05-21 DOI: 10.1007/s10455-025-10001-8
Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
{"title":"Dimension reduction for positively curved steady solitons","authors":"Pak-Yeung Chan,&nbsp;Zilu Ma,&nbsp;Yongjia Zhang","doi":"10.1007/s10455-025-10001-8","DOIUrl":"10.1007/s10455-025-10001-8","url":null,"abstract":"<div><p>We consider noncollapsed steady gradient Ricci solitons with nonnegative sectional curvature. We show that such solitons always dimension reduce at infinity. This generalizes an earlier result in [19] to higher dimensions. In dimension four, we classify possible reductions at infinity, which lays foundation for possible classifications of steady solitons. Moreover, we show that any tangent flow at infinity of a general noncollapsed steady soliton must split off a line. This generalizes an earlier result in [7] to higher dimensions. While this article is under preparation, we realized that part of our main results are proved independently in a recent post [42] under different assumptions.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144100151","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
Rigidity of Einstein manifolds with positive Yamabe invariant 具有正Yamabe不变量的爱因斯坦流形的刚性
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-05-21 DOI: 10.1007/s10455-025-09996-x
L. Branca, G. Catino, D. Dameno, P. Mastrolia
{"title":"Rigidity of Einstein manifolds with positive Yamabe invariant","authors":"L. Branca,&nbsp;G. Catino,&nbsp;D. Dameno,&nbsp;P. Mastrolia","doi":"10.1007/s10455-025-09996-x","DOIUrl":"10.1007/s10455-025-09996-x","url":null,"abstract":"<div><p>We provide optimal pinching results on closed Einstein manifolds with positive Yamabe invariant in any dimension, extending the optimal bound for the scalar curvature due to Gursky and LeBrun in dimension four. We also improve the known bounds of the Yamabe invariant <i>via</i> the <span>(L^{frac{n}{2}})</span>-norm of the Weyl tensor for low-dimensional Einstein manifolds. Finally, we discuss some advances on an algebraic inequality involving the Weyl tensor for dimensions 5 and 6.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-025-09996-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144108510","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
Random 3-manifolds have no totally geodesic submanifolds 随机3-流形没有完全测地线子流形
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-05-15 DOI: 10.1007/s10455-025-09998-9
Hasan M. El-Hasan, Frederick Wilhelm
{"title":"Random 3-manifolds have no totally geodesic submanifolds","authors":"Hasan M. El-Hasan,&nbsp;Frederick Wilhelm","doi":"10.1007/s10455-025-09998-9","DOIUrl":"10.1007/s10455-025-09998-9","url":null,"abstract":"<div><p>Murphy and the second author showed that a generic closed Riemannian manifold has no totally geodesic submanifolds, provided the ambient space is at least four dimensional. Lytchak and Petrunin established a similar result in dimension 3. For the higher dimensional result, the “generic set” is open and dense in the <span>(C^{q})</span>–topology for any <span>(qge 2.)</span> In Lytchak and Petrunin’s work, the “generic set” is a dense <span>(G_{delta })</span> in the <span>(C^{q})</span>–topology for any <span>(qge 2.)</span> Here we show that the set of such metrics on a compact 3–manifold actually contains a set that is that is open and dense set in the <span>(C^{q})</span>–topology, provided <span>(qge 3.)</span></p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-025-09998-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143949638","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
Symmetries of (2, 3, 5)-distributions and associated Legendrian cone structures （2,3,5）-分布及其相关Legendrian锥结构的对称性
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-04-30 DOI: 10.1007/s10455-025-09992-1
Jun-Muk Hwang, Dennis The
{"title":"Symmetries of (2, 3, 5)-distributions and associated Legendrian cone structures","authors":"Jun-Muk Hwang,&nbsp;Dennis The","doi":"10.1007/s10455-025-09992-1","DOIUrl":"10.1007/s10455-025-09992-1","url":null,"abstract":"<div><p>We exploit a natural correspondence between holomorphic (2, 3, 5)-distributions and nondegenerate lines on holomorphic contact manifolds of dimension 5 to present a new perspective in the study of symmetries of (2, 3, 5)-distributions. This leads to a number of new results in this classical subject, including an unexpected relation between the multiply-transitive families of models having 7- and 6-dimensional symmetries, and a one-to-one correspondence between equivalence classes of nontransitive (2, 3, 5)-distributions with 6-dimensional symmetries and nonhomogeneous nondegenerate Legendrian curves in <span>({{mathbb {P}}}^3)</span>. An ingredient for establishing the former is an explicit classification of homogeneous nondegenerate Legendrian curves in <span>({{mathbb {P}}}^3)</span>, which we present. Moreover, our approach gives a new perspective on exceptionality of the 3 : 1 ratio for two 2-spheres rolling on each other without twisting or slipping.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-025-09992-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143892670","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
Correction to: Compact Kähler surfaces with trivial canonical bundle 修正：压缩Kähler曲面与平凡规范束
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-04-24 DOI: 10.1007/s10455-025-09997-w
Nicholas Buchdahl
{"title":"Correction to: Compact Kähler surfaces with trivial canonical bundle","authors":"Nicholas Buchdahl","doi":"10.1007/s10455-025-09997-w","DOIUrl":"10.1007/s10455-025-09997-w","url":null,"abstract":"","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143871371","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 periodic Plateau problem and its application 周期性高原问题及其应用
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-04-13 DOI: 10.1007/s10455-025-09993-0
Jaigyoung Choe
{"title":"The periodic Plateau problem and its application","authors":"Jaigyoung Choe","doi":"10.1007/s10455-025-09993-0","DOIUrl":"10.1007/s10455-025-09993-0","url":null,"abstract":"<div><p>Given a noncompact disconnected periodic curve <span>(Gamma )</span> of infinite length with two components and no self-intersection in <span>(mathbb R^3)</span>, it is proved that there exists a noncompact simply connected periodic minimal surface spanning <span>(Gamma )</span>. As an application, it is shown that for any tetrahedron <i>T</i> with dihedral angles <span>(le 90^circ )</span>, there exist four embedded minimal annuli in <i>T</i>, which are perpendicular to <span>(partial T)</span> along their boundary. It is also proved that every Platonic solid of <span>(mathbb R^3)</span> contains a free boundary embedded minimal surface of genus zero.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143826576","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 moduli space of flat maximal space-like embeddings in pseudo-hyperbolic space 伪双曲空间中平面极大类空嵌入的模空间
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-04-03 DOI: 10.1007/s10455-025-09994-z
Nicholas Rungi, Andrea Tamburelli
{"title":"The moduli space of flat maximal space-like embeddings in pseudo-hyperbolic space","authors":"Nicholas Rungi,&nbsp;Andrea Tamburelli","doi":"10.1007/s10455-025-09994-z","DOIUrl":"10.1007/s10455-025-09994-z","url":null,"abstract":"<div><p>We study the moduli space of flat maximal space-like embeddings in <span>({mathbb {H}}^{2,2})</span> from various aspects. We first describe the associated Codazzi tensors to the embedding in the general setting, and then, we introduce a family of pseudo-Kähler metrics on the moduli space. We show the existence of two Hamiltonian actions with associated moment maps and use them to find a geometric global Darboux frame for any symplectic form in the above family.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-025-09994-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769821","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
Toric Einstein 4-manifolds with non-negative sectional curvature 具有非负截面曲率的环面爱因斯坦4流形
IF 0.6 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2025-04-02 DOI: 10.1007/s10455-025-09990-3
Tianyue Liu
{"title":"Toric Einstein 4-manifolds with non-negative sectional curvature","authors":"Tianyue Liu","doi":"10.1007/s10455-025-09990-3","DOIUrl":"10.1007/s10455-025-09990-3","url":null,"abstract":"<div><p>We prove that <span>(T^2)</span>-invariant Einstein metrics with non-negative sectional curvature on a four-manifold are locally symmetric.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-025-09990-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761720","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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