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Annals of Global Analysis and Geometry最新文献

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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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
On the intrinsic and extrinsic boundary for metric measure spaces with lower curvature bounds 关于曲率下界度量测度空间的内外边界
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-08-31 DOI: 10.1007/s10455-023-09920-1
Vitali Kapovitch, Xingyu Zhu
{"title":"On the intrinsic and extrinsic boundary for metric measure spaces with lower curvature bounds","authors":"Vitali Kapovitch,&nbsp;Xingyu Zhu","doi":"10.1007/s10455-023-09920-1","DOIUrl":"10.1007/s10455-023-09920-1","url":null,"abstract":"<div><p>We show that if an Alexandrov space <i>X</i> has an Alexandrov subspace <span>({bar{Omega }})</span> of the same dimension disjoint from the boundary of <i>X</i>, then the topological boundary of <span>({bar{Omega }})</span> coincides with its Alexandrov boundary. Similarly, if a noncollapsed <span>({{,textrm{RCD},}}(K,N))</span> space <i>X</i> has a noncollapsed <span>({{,textrm{RCD},}}(K,N))</span> subspace <span>({bar{Omega }})</span> disjoint from boundary of <i>X</i> and with mild boundary condition, then the topological boundary of <span>({bar{Omega }})</span> coincides with its De Philippis–Gigli boundary. We then discuss some consequences about convexity of such type of equivalence.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44849525","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
Hadamard expansions for powers of causal Green’s operators and “resolvents” 因果格林算子幂的Hadamard展开式与“解”
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-08-29 DOI: 10.1007/s10455-023-09921-0
Lennart Ronge
{"title":"Hadamard expansions for powers of causal Green’s operators and “resolvents”","authors":"Lennart Ronge","doi":"10.1007/s10455-023-09921-0","DOIUrl":"10.1007/s10455-023-09921-0","url":null,"abstract":"<div><p>The Hadamard expansion describes the singularity structure of Green’s operators associated with a normally hyperbolic operator <i>P</i> in terms of Riesz distributions (fundamental solutions on Minkowski space, transported to the manifold via the exponential map) and Hadamard coefficients (smooth sections in two variables, corresponding to the heat Kernel coefficients in the Riemannian case). In this paper, we derive an asymptotic expansion analogous to the Hadamard expansion for powers of advanced/retarded Green’s operators associated with <i>P</i>, as well as expansions for advanced/retarded Green’s operators associated with <span>(P-z)</span> for <span>(zin mathbb {C})</span>. These expansions involve the same Hadamard coefficients as the original Hadamard expansion, as well as the same or analogous (with built-in <i>z</i>-dependence) Riesz distributions.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09921-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46544751","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
Explicit harmonic morphisms and p-harmonic functions from the complex and quaternionic Grassmannians 复格拉斯曼和四元数格拉斯曼的显调和态射和p-调和函数
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-08-24 DOI: 10.1007/s10455-023-09919-8
Elsa Ghandour, Sigmundur Gudmundsson
{"title":"Explicit harmonic morphisms and p-harmonic functions from the complex and quaternionic Grassmannians","authors":"Elsa Ghandour,&nbsp;Sigmundur Gudmundsson","doi":"10.1007/s10455-023-09919-8","DOIUrl":"10.1007/s10455-023-09919-8","url":null,"abstract":"<div><p>We construct explicit complex-valued <i>p</i>-harmonic functions and harmonic morphisms on the classical compact symmetric complex and quaternionic Grassmannians. The ingredients for our construction method are joint eigenfunctions of the classical Laplace–Beltrami and the so-called conformality operator. A known duality principle implies that these <i>p</i>-harmonic functions and harmonic morphisms also induce such solutions on the Riemannian symmetric non-compact dual spaces.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09919-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47135168","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
Quantitative version of Weyl’s law 魏尔定律的定量版本
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-08-20 DOI: 10.1007/s10455-023-09922-z
Nikhil Savale
{"title":"Quantitative version of Weyl’s law","authors":"Nikhil Savale","doi":"10.1007/s10455-023-09922-z","DOIUrl":"10.1007/s10455-023-09922-z","url":null,"abstract":"<div><p>We prove a general estimate for the Weyl remainder of an elliptic, semiclassical pseudodifferential operator in terms of volumes of recurrence sets for the Hamilton flow of its principal symbol. This quantifies earlier results of Volovoy (Comm Partial Differential Equations 15:1509–1563, 1990; Ann Global Anal Geom 8:127–136, 1990). Our result particularly improves Weyl remainder exponents for compact Lie groups and surfaces of revolution. And gives a quantitative estimate for Bérard’s Weyl remainder in terms of the maximal expansion rate and topological entropy of the geodesic flow.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09922-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46270493","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
Almost contact metric manifolds with certain condition 具有一定条件的几乎接触度量流形
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-08-08 DOI: 10.1007/s10455-023-09917-w
Benaoumeur Bayour, Gherici Beldjilali, Moulay Larbi Sinacer
{"title":"Almost contact metric manifolds with certain condition","authors":"Benaoumeur Bayour,&nbsp;Gherici Beldjilali,&nbsp;Moulay Larbi Sinacer","doi":"10.1007/s10455-023-09917-w","DOIUrl":"10.1007/s10455-023-09917-w","url":null,"abstract":"<div><p>The object of this article is to study a new class of almost contact metric structures which are integrable but non normal. Secondly, we explain a method of construction for normal manifold starting from a non-normal but integrable manifold. Illustrative examples are given.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48557029","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
Greatest Ricci lower bounds of projective horospherical manifolds of Picard number one Picard数1的投影球面流形的最大Ricci下界
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-08-08 DOI: 10.1007/s10455-023-09915-y
DongSeon Hwang, Shin-young Kim, Kyeong-Dong Park
{"title":"Greatest Ricci lower bounds of projective horospherical manifolds of Picard number one","authors":"DongSeon Hwang,&nbsp;Shin-young Kim,&nbsp;Kyeong-Dong Park","doi":"10.1007/s10455-023-09915-y","DOIUrl":"10.1007/s10455-023-09915-y","url":null,"abstract":"<div><p>A horospherical variety is a normal <i>G</i>-variety such that a connected reductive algebraic group <i>G</i> acts with an open orbit isomorphic to a torus bundle over a rational homogeneous manifold. The projective horospherical manifolds of Picard number one are classified by Pasquier, and it turned out that the automorphism groups of all nonhomogeneous ones are non-reductive, which implies that they admit no Kähler–Einstein metrics. As a numerical measure of the extent to which a Fano manifold is close to be Kähler–Einstein, we compute the greatest Ricci lower bounds of projective horospherical manifolds of Picard number one using the barycenter of each moment polytope with respect to the Duistermaat–Heckman measure based on a recent work of Delcroix and Hultgren. In particular, the greatest Ricci lower bound of the odd symplectic Grassmannian <span>(text {SGr}(n,2n+1))</span> can be arbitrarily close to zero as <i>n</i> grows.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09915-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41914696","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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