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Annals of Global Analysis and Geometry最新文献

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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":"64 2","pages":""},"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":"64 2","pages":""},"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":"64 2","pages":""},"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":"64 2","pages":""},"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":"64 2","pages":""},"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":"64 2","pages":""},"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
Prescribed mean curvature flow of non-compact space-like Cauchy hypersurfaces 非紧化类空柯西超曲面的规定平均曲率流
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-08-02 DOI: 10.1007/s10455-023-09914-z
Giuseppe Gentile, Boris Vertman
{"title":"Prescribed mean curvature flow of non-compact space-like Cauchy hypersurfaces","authors":"Giuseppe Gentile,&nbsp;Boris Vertman","doi":"10.1007/s10455-023-09914-z","DOIUrl":"10.1007/s10455-023-09914-z","url":null,"abstract":"<div><p>In this paper we consider the prescribed mean curvature flow of a non-compact space-like Cauchy hypersurface of bounded geometry in a generalized Robertson–Walker space-time. We prove that the flow preserves the space-likeness condition and exists for infinite time. We also prove convergence in the setting of manifolds with boundary. Our discussion generalizes previous work by Ecker, Huisken, Gerhardt and others with respect to a crucial aspects: we consider any non-compact Cauchy hypersurface under the assumption of bounded geometry. Moreover, we specialize the aforementioned works by considering globally hyperbolic Lorentzian space-times equipped with a specific class of warped product metrics.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09914-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43221696","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
The metric completion of the space of vector-valued one-forms 向量值一空间的度量完备形式
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-08-01 DOI: 10.1007/s10455-023-09916-x
Nicola Cavallucci, Zhe Su
{"title":"The metric completion of the space of vector-valued one-forms","authors":"Nicola Cavallucci,&nbsp;Zhe Su","doi":"10.1007/s10455-023-09916-x","DOIUrl":"10.1007/s10455-023-09916-x","url":null,"abstract":"<div><p>The space of full-ranked one-forms on a smooth, orientable, compact manifold (possibly with boundary) is metrically incomplete with respect to the induced geodesic distance of the generalized Ebin metric. We show a distance equality between the induced geodesic distances of the generalized Ebin metric on the space of full-ranked one-forms and the corresponding Riemannian metric defined on each fiber. Using this result, we immediately have a concrete description of the metric completion of the space of full-ranked one-forms. Additionally, we study the relationship between the space of full-ranked one-forms and the space of all Riemannian metrics, leading to quotient structures for the space of Riemannian metrics and its completion.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09916-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43550124","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
Products of manifolds with fibered corners 纤维角管产品
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-07-27 DOI: 10.1007/s10455-023-09912-1
Chris Kottke, Frédéric Rochon
{"title":"Products of manifolds with fibered corners","authors":"Chris Kottke,&nbsp;Frédéric Rochon","doi":"10.1007/s10455-023-09912-1","DOIUrl":"10.1007/s10455-023-09912-1","url":null,"abstract":"<div><p>Manifolds with fibered corners arise as resolutions of stratified spaces, as ‘many-body’ compactifications of vector spaces, and as compactifications of certain moduli spaces including those of non-abelian Yang–Mills–Higgs monopoles, among other settings. However, Cartesian products of manifolds with fibered corners do not generally have fibered corners themselves and thus fail to reflect the appropriate structure of products of the underlying spaces in the above settings. Here, we determine a resolution of the Cartesian product of fibered corners manifolds by blow-up which we call the ‘ordered product,’ which leads to a well-behaved category of fibered corners manifolds in which the ordered product satisfies the appropriate universal property. In contrast to the usual category of manifolds with corners, this category of fibered corners not only has all finite products, but all finite transverse fiber products as well, and we show in addition that the ordered product is a natural product for wedge (aka incomplete edge) metrics and quasi-fibered boundary metrics, a class which includes QAC and QALE metrics.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48427153","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
Anticanonically balanced metrics and the Hilbert–Mumford criterion for the (delta _m)-invariant of Fujita–Odaka Fujita–Odaka的（delta _m）-不变量的反对称平衡度量和Hilbert–Mumford准则
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-07-12 DOI: 10.1007/s10455-023-09911-2
Yoshinori Hashimoto
{"title":"Anticanonically balanced metrics and the Hilbert–Mumford criterion for the (delta _m)-invariant of Fujita–Odaka","authors":"Yoshinori Hashimoto","doi":"10.1007/s10455-023-09911-2","DOIUrl":"10.1007/s10455-023-09911-2","url":null,"abstract":"<div><p>We prove that the stability condition for Fano manifolds defined by Saito–Takahashi, given in terms of the sum of the Ding invariant and the Chow weight, is equivalent to the existence of anticanonically balanced metrics. Combined with the result by Rubinstein–Tian–Zhang, we obtain the following algebro-geometric corollary: the <span>(delta _m)</span>-invariant of Fujita–Odaka satisfies <span>(delta _m &gt;1)</span> if and only if the Fano manifold is stable in the sense of Saito–Takahashi, establishing a Hilbert–Mumford-type criterion for <span>(delta _m &gt;1)</span>. We also extend this result to the Kähler–Ricci <i>g</i>-solitons and the coupled Kähler–Einstein metrics, and as a by-product we obtain a formula for the asymptotic slope of the coupled Ding functional in terms of multiple test configurations.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"64 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50475107","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
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