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Annals of Global Analysis and Geometry最新文献

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Dispersive equations on asymptotically conical manifolds: time decay in the low-frequency regime 渐近圆锥流形上的色散方程:低频区的时间衰减
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-03-06 DOI: 10.1007/s10455-023-09887-z
Viviana Grasselli
{"title":"Dispersive equations on asymptotically conical manifolds: time decay in the low-frequency regime","authors":"Viviana Grasselli","doi":"10.1007/s10455-023-09887-z","DOIUrl":"10.1007/s10455-023-09887-z","url":null,"abstract":"<div><p>On an asymptotically conical manifold, we prove time decay estimates for the flow of the Schrödinger wave and Klein–Gordon equations via some differentiability properties of the spectral measure. To keep the paper at a reasonable length, we limit ourselves to the low-energy part of the spectrum, which is the one that dictates the decay rates. With this paper, we extend sharp estimates that are known in the asymptotically flat case (see Bouclet and Burq in Duke Math J 170(11):2575–2629, 2021, https://doi.org/10.1215/00127094-2020-0080) to this more general geometric framework and therefore recover the same decay properties as in the Euclidean case. The first step is to prove some resolvent estimates via a limiting absorption principle. It is at this stage that the proof of the previously mentioned authors fails, in particular when we try to recover a low-frequency positive commutator estimate. Once the resolvent estimates are established, we derive regularity for the spectral measure that in turn is applied to obtain the decay of the flows.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09887-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47503903","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: Besse conjecture with positive isotropic curvature 修正：具有正各向同性曲率的Besse猜想
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-03-02 DOI: 10.1007/s10455-023-09892-2
Seungsu Hwang, Gabjin Yun
{"title":"Correction to: Besse conjecture with positive isotropic curvature","authors":"Seungsu Hwang,&nbsp;Gabjin Yun","doi":"10.1007/s10455-023-09892-2","DOIUrl":"10.1007/s10455-023-09892-2","url":null,"abstract":"","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45678275","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
Classification of left-invariant Einstein metrics on (textrm{SL}(2,mathbb {R})times textrm{SL}(2,mathbb {R})) that are bi-invariant under a one-parameter subgroup 单参数子群下双不变的（textrm｛SL｝（2，mathbb｛R｝）timestextrm{SL｝
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-03-02 DOI: 10.1007/s10455-023-09890-4
Vicente Cortés, Jeremias Ehlert, Alexander S. Haupt, David Lindemann
{"title":"Classification of left-invariant Einstein metrics on (textrm{SL}(2,mathbb {R})times textrm{SL}(2,mathbb {R})) that are bi-invariant under a one-parameter subgroup","authors":"Vicente Cortés,&nbsp;Jeremias Ehlert,&nbsp;Alexander S. Haupt,&nbsp;David Lindemann","doi":"10.1007/s10455-023-09890-4","DOIUrl":"10.1007/s10455-023-09890-4","url":null,"abstract":"<div><p>We classify all left-invariant pseudo-Riemannian Einstein metrics on <span>(textrm{SL}(2,mathbb {R})times textrm{SL}(2,mathbb {R}))</span> that are bi-invariant under a one-parameter subgroup. We find that there are precisely two such metrics up to homothety, the Killing form and a nearly pseudo-Kähler metric.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09890-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50441997","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: Hypercohomologies of truncated twisted holomorphic de Rham complexes 对截断扭曲全纯de Rham复合物的超上同调的修正
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-02-27 DOI: 10.1007/s10455-023-09891-3
Lingxu Meng
{"title":"Correction to: Hypercohomologies of truncated twisted holomorphic de Rham complexes","authors":"Lingxu Meng","doi":"10.1007/s10455-023-09891-3","DOIUrl":"10.1007/s10455-023-09891-3","url":null,"abstract":"","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50517371","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 results for Riemannian twistor spaces under vanishing curvature conditions 曲率消失条件下黎曼扭转空间的刚度结果
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-02-23 DOI: 10.1007/s10455-023-09889-x
G. Catino, D. Dameno, P. Mastrolia
{"title":"Rigidity results for Riemannian twistor spaces under vanishing curvature conditions","authors":"G. Catino,&nbsp;D. Dameno,&nbsp;P. Mastrolia","doi":"10.1007/s10455-023-09889-x","DOIUrl":"10.1007/s10455-023-09889-x","url":null,"abstract":"<div><p>In this paper, we provide new rigidity results for four-dimensional Riemannian manifolds and their twistor spaces. In particular, using the moving frame method, we prove that <span>(mathbb {C}mathbb {P}^3)</span> is the only twistor space whose Bochner tensor is parallel; moreover, we classify Hermitian Ricci-parallel and locally symmetric twistor spaces and we show the nonexistence of conformally flat twistor spaces. We also generalize a result due to Atiyah, Hitchin and Singer concerning the self-duality of a Riemannian four-manifold.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09889-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44737636","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
Gauss maps of harmonic and minimal great circle fibrations 调和和最小大圆振动的高斯图
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-02-13 DOI: 10.1007/s10455-023-09886-0
Ioannis Fourtzis, Michael Markellos, Andreas Savas-Halilaj
{"title":"Gauss maps of harmonic and minimal great circle fibrations","authors":"Ioannis Fourtzis,&nbsp;Michael Markellos,&nbsp;Andreas Savas-Halilaj","doi":"10.1007/s10455-023-09886-0","DOIUrl":"10.1007/s10455-023-09886-0","url":null,"abstract":"<div><p>We investigate Gauss maps associated to great circle fibrations of the euclidean unit 3-sphere <span>(mathbb {S}^3)</span>. We show that the associated Gauss map to such a fibration is harmonic, respectively minimal, if and only if the unit vector field generating the great circle foliation is harmonic, respectively minimal. These results can be viewed as analogues of the classical theorem of Ruh and Vilms about the harmonicity of the Gauss map of a minimal submanifold in the euclidean space. Moreover, we prove that a harmonic or minimal unit vector field on <span>(mathbb {S}^3)</span>, whose integral curves are great circles, is a Hopf vector field.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09886-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47929403","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
Multiple solutions for Schrödinger equations on Riemannian manifolds via (nabla )-theorems 黎曼流形上Schrödinger方程的多解及其$$nabla$$Ş-定理
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-01-24 DOI: 10.1007/s10455-023-09885-1
Luigi Appolloni, Giovanni Molica Bisci, Simone Secchi
{"title":"Multiple solutions for Schrödinger equations on Riemannian manifolds via (nabla )-theorems","authors":"Luigi Appolloni,&nbsp;Giovanni Molica Bisci,&nbsp;Simone Secchi","doi":"10.1007/s10455-023-09885-1","DOIUrl":"10.1007/s10455-023-09885-1","url":null,"abstract":"<div><p>We consider a smooth, complete and non-compact Riemannian manifold <span>((mathcal {M},g))</span> of dimension <span>(d ge 3)</span>, and we look for solutions to the semilinear elliptic equation </p><div><div><span>$$begin{aligned} -varDelta _g w + V(sigma ) w = alpha (sigma ) f(w) + lambda w quad hbox {in }mathcal {M}. end{aligned}$$</span></div></div><p>The potential <span>(V :mathcal {M} rightarrow mathbb {R})</span> is a continuous function which is coercive in a suitable sense, while the nonlinearity <i>f</i> has a subcritical growth in the sense of Sobolev embeddings. By means of <span>(nabla )</span>-theorems introduced by Marino and Saccon, we prove that at least three non-trivial solutions exist as soon as the parameter <span>(lambda )</span> is sufficiently close to an eigenvalue of the operator <span>(-varDelta _g)</span>.\u0000</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49143954","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 Steklov spectrum of covering spaces and total spaces 关于覆盖空间和全空间的Steklov谱
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-01-17 DOI: 10.1007/s10455-023-09884-2
Panagiotis Polymerakis
{"title":"On the Steklov spectrum of covering spaces and total spaces","authors":"Panagiotis Polymerakis","doi":"10.1007/s10455-023-09884-2","DOIUrl":"10.1007/s10455-023-09884-2","url":null,"abstract":"<div><p>We show the existence of a natural Dirichlet-to-Neumann map on Riemannian manifolds with boundary and bounded geometry, such that the bottom of the Dirichlet spectrum is positive. This map regarded as a densely defined operator in the <span>(L^2)</span>-space of the boundary admits Friedrichs extension. We focus on the spectrum of this operator on covering spaces and total spaces of Riemannian principal bundles over compact manifolds.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09884-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41604374","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
Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces 二维和三维双曲空间上齐次向量丛截面的Delorme交织条件
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2022-12-05 DOI: 10.1007/s10455-022-09882-w
Martin Olbrich, Guendalina Palmirotta
{"title":"Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces","authors":"Martin Olbrich,&nbsp;Guendalina Palmirotta","doi":"10.1007/s10455-022-09882-w","DOIUrl":"10.1007/s10455-022-09882-w","url":null,"abstract":"<div><p>The description of the Paley–Wiener space for compactly supported smooth functions <span>(C^infty _c(G))</span> on a semi-simple Lie group <i>G</i> involves certain intertwining conditions that are difficult to handle. In the present paper, we make them completely explicit for <span>(G=textbf{SL}(2,mathbb {R})^d)</span> (<span>(din mathbb {N})</span>) and <span>(G=textbf{SL}(2,mathbb {C}))</span>. Our results are based on a defining criterion for the Paley–Wiener space, valid for general groups of real rank one, that we derive from Delorme’s proof of the Paley–Wiener theorem. In a forthcoming paper, we will show how these results can be used to study solvability of invariant differential operators between sections of homogeneous vector bundles over the corresponding symmetric spaces.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49570414","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
On the eigenforms of compact stratified spaces 关于紧致分层空间的本征形式
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2022-11-24 DOI: 10.1007/s10455-022-09883-9
Luobin Fang
{"title":"On the eigenforms of compact stratified spaces","authors":"Luobin Fang","doi":"10.1007/s10455-022-09883-9","DOIUrl":"10.1007/s10455-022-09883-9","url":null,"abstract":"<div><p>Let <i>X</i> be a compact Thom–Mather stratified pseudomanifold, and let <i>M</i> be the regular part of <i>X</i> endowed with an iterated metric. In this paper, we prove that if the curvature operator of <i>M</i> is bounded, then the <span>(L^2)</span> harmonic space of <i>M</i> is finite dimensional. Next we consider the absolute eigenvalue problems of the Hodge Laplacian of a sequence of compact domains <span>(Omega _j)</span> converging to <i>M</i>. We prove that when the curvature operator of <i>M</i> is bounded, the eigenvalues of <span>(Omega _j)</span> converge to eigenvalues of <i>M</i>, and the eigenforms of <span>(Omega _j)</span> converge to eigenforms of <i>M</i> in the Sobolev norm. This generalizes Chavel and Feldman’s theorem in Chavel and Feldman (J Funct Anal 30:198-222, 1978) from compact manifolds to compact pseudomanifolds and from functions to differential forms. Then, we apply our results to <span>(L^2)</span>-chomology. We will give a correspondence between boundary cohomology and <span>(L^2)</span>-cohomology.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45120432","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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