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Annals of Global Analysis and Geometry最新文献

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Sobolev inequalities and convergence for Riemannian metrics and distance functions 黎曼度量和距离函数的Sobolev不等式和收敛性
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-06-01 DOI: 10.1007/s10455-023-09906-z
B. Allen, E. Bryden
{"title":"Sobolev inequalities and convergence for Riemannian metrics and distance functions","authors":"B. Allen,&nbsp;E. Bryden","doi":"10.1007/s10455-023-09906-z","DOIUrl":"10.1007/s10455-023-09906-z","url":null,"abstract":"<div><p>If one thinks of a Riemannian metric, <span>(g_1)</span>, analogously as the gradient of the corresponding distance function, <span>(d_1)</span>, with respect to a background Riemannian metric, <span>(g_0)</span>, then a natural question arises as to whether a corresponding theory of Sobolev inequalities exists between the Riemannian metric and its distance function. In this paper, we study the sub-critical case <span>(p &lt; frac{m}{2})</span> where we show a Sobolev inequality exists between a Riemannian metric and its distance function. In particular, we show that an <span>(L^{frac{p}{2}})</span> bound on a Riemannian metric implies an <span>(L^q)</span> bound on its corresponding distance function. We then use this result to state a convergence theorem and show how this theorem can be useful to prove geometric stability results by proving a version of Gromov’s conjecture for tori with almost non-negative scalar curvature in the conformal case. Examples are given to show that the hypotheses of the main theorems are necessary.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43867965","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: 2
On non-compact gradient solitons 关于非紧化梯度孤子
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-05-24 DOI: 10.1007/s10455-023-09904-1
Antonio W. Cunha, Erin Griffin
{"title":"On non-compact gradient solitons","authors":"Antonio W. Cunha,&nbsp;Erin Griffin","doi":"10.1007/s10455-023-09904-1","DOIUrl":"10.1007/s10455-023-09904-1","url":null,"abstract":"<div><p>In this paper, we extend existing results for generalized solitons, called <i>q</i>-solitons, to the complete case by considering non-compact solitons. By placing regularity conditions on the vector field <i>X</i> and curvature conditions on <i>M</i>, we are able to use the chosen properties of the tensor <i>q</i> to see that such non-compact <i>q</i>-solitons are stationary and <i>q</i>-flat. We conclude by applying our results to the examples of ambient obstruction solitons, Cotton solitons, and Bach solitons to demonstrate the utility of these general theorems for various flows.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42518816","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
Laplace eigenvalues of ellipsoids obtained as analytic perturbations of the unit sphere 单位球的解析摄动得到椭球的拉普拉斯特征值
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-04-25 DOI: 10.1007/s10455-023-09901-4
Anandateertha G. Mangasuli, Aditya Tiwari
{"title":"Laplace eigenvalues of ellipsoids obtained as analytic perturbations of the unit sphere","authors":"Anandateertha G. Mangasuli,&nbsp;Aditya Tiwari","doi":"10.1007/s10455-023-09901-4","DOIUrl":"10.1007/s10455-023-09901-4","url":null,"abstract":"<div><p>The Euclidean unit sphere in dimension <i>n</i> minimizes the first positive eigenvalue of the Laplacian among all the compact, Riemannian manifolds of dimension <i>n</i> with Ricci curvature bounded below by <span>(n-1)</span> as a consequence of Lichnerowicz’s theorem. The eigenspectrum of the Laplacian is given by a non-decreasing sequence of real numbers tending to infinity. In dimension two, we prove that such an inequality holds for the subsequent eigenvalues in the sequence for ellipsoids that are obtained as analytic perturbations of the Euclidean unit sphere for the truncated spectrum.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45877068","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
Remarks on astheno-Kähler manifolds, Bott-Chern and Aeppli cohomology groups 关于软Kähler流形、Bott-Chern和Aeppli上同调群的注记
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-04-24 DOI: 10.1007/s10455-023-09903-2
Ionuţ Chiose, Rareş Răsdeaconu
{"title":"Remarks on astheno-Kähler manifolds, Bott-Chern and Aeppli cohomology groups","authors":"Ionuţ Chiose,&nbsp;Rareş Răsdeaconu","doi":"10.1007/s10455-023-09903-2","DOIUrl":"10.1007/s10455-023-09903-2","url":null,"abstract":"<div><p>We provide a new cohomological obstruction to the existence of astheno-Kähler metrics on compact complex manifolds. Several results of independent interests regarding the Bott-Chern and Aeppli cohomology groups are presented and relevant examples are discussed.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09903-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41895506","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
Pseudo-Kähler and pseudo-Sasaki structures on Einstein solvmanifolds Pseudo-Kähler和爱因斯坦解流形上的伪sasaki结构
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-04-24 DOI: 10.1007/s10455-023-09894-0
Diego Conti, Federico Alberto Rossi, Romeo Segnan Dalmasso
{"title":"Pseudo-Kähler and pseudo-Sasaki structures on Einstein solvmanifolds","authors":"Diego Conti,&nbsp;Federico Alberto Rossi,&nbsp;Romeo Segnan Dalmasso","doi":"10.1007/s10455-023-09894-0","DOIUrl":"10.1007/s10455-023-09894-0","url":null,"abstract":"<div><p>The aim of this paper is to construct left-invariant Einstein pseudo-Riemannian Sasaki metrics on solvable Lie groups. We consider the class of <span>(mathfrak {z})</span>-standard Sasaki solvable Lie algebras of dimension <span>(2n+3)</span>, which are in one-to-one correspondence with pseudo-Kähler nilpotent Lie algebras of dimension 2<i>n</i> endowed with a compatible derivation, in a suitable sense. We characterize the pseudo-Kähler structures and derivations giving rise to Sasaki–Einstein metrics. We classify <span>(mathfrak {z})</span>-standard Sasaki solvable Lie algebras of dimension <span>(le 7)</span> and those whose pseudo-Kähler reduction is an abelian Lie algebra. The Einstein metrics we obtain are standard, but not of pseudo-Iwasawa type.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09894-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47369709","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
Normalized Yamabe flow on manifolds with bounded geometry 几何有界流形上的归一化Yamabe流
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-04-19 DOI: 10.1007/s10455-023-09902-3
Bruno Caldeira, Luiz Hartmann, Boris Vertman
{"title":"Normalized Yamabe flow on manifolds with bounded geometry","authors":"Bruno Caldeira,&nbsp;Luiz Hartmann,&nbsp;Boris Vertman","doi":"10.1007/s10455-023-09902-3","DOIUrl":"10.1007/s10455-023-09902-3","url":null,"abstract":"<div><p>The goal of this paper is to study Yamabe flow on a complete Riemannian manifold of bounded geometry with possibly infinite volume. In case of infinite volume, standard volume normalization of the Yamabe flow fails and the flow may not converge. Instead, we consider a curvature normalized Yamabe flow, and assuming negative scalar curvature, prove its long-time existence and convergence. This extends the results of Suárez-Serrato and Tapie to a non-compact setting. In the appendix we specify our analysis to a particular example of manifolds with bounded geometry, namely manifolds with fibered boundary metric. In this case we obtain stronger estimates for the short time solution using microlocal methods.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09902-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44015268","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
Kummer-type constructions of almost Ricci-flat 5-manifolds 几乎Ricci平坦5流形的Kummer型构造
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-04-13 DOI: 10.1007/s10455-023-09900-5
Chanyoung Sung
{"title":"Kummer-type constructions of almost Ricci-flat 5-manifolds","authors":"Chanyoung Sung","doi":"10.1007/s10455-023-09900-5","DOIUrl":"10.1007/s10455-023-09900-5","url":null,"abstract":"<div><p>A smooth closed manifold <i>M</i> is called almost Ricci-flat if </p><div><div><span>$$begin{aligned} inf _g||text {Ric}_g||_infty cdot text {diam}_g(M)^2=0 end{aligned}$$</span></div></div><p>where <span>(text {Ric}_g)</span> and <span>(text {diam}_g)</span>, respectively, denote the Ricci tensor and the diameter of <i>g</i> and <i>g</i> runs over all Riemannian metrics on <i>M</i>. By using Kummer-type method, we construct a smooth closed almost Ricci-flat nonspin 5-manifold <i>M</i> which is simply connected. It is minimal volume vanishes; namely, it collapses with sectional curvature bounded.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09900-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45084153","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
The Lax equation and weak regularity of asymptotic estimate Lie groups 渐近估计李群的Lax方程和弱正则性
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-04-05 DOI: 10.1007/s10455-023-09888-y
Maximilian Hanusch
{"title":"The Lax equation and weak regularity of asymptotic estimate Lie groups","authors":"Maximilian Hanusch","doi":"10.1007/s10455-023-09888-y","DOIUrl":"10.1007/s10455-023-09888-y","url":null,"abstract":"<div><p>We investigate the Lax equation in the context of infinite-dimensional Lie algebras. Explicit solutions are discussed in the sequentially complete asymptotic estimate context, and an integral expansion (sums of iterated Riemann integrals over nested commutators with correction term) is derived for the situation that the Lie algebra is inherited by an infinite-dimensional Lie group in Milnor’s sense. In the context of Banach Lie groups (and Lie groups with suitable regularity properties), we generalize the Baker–Campbell–Dynkin–Hausdorff formula to the product integral (with additional nilpotency assumption in the non-Banach case). We combine this formula with the results obtained for the Lax equation to derive an explicit representation of the product integral in terms of the exponential map. An important ingredient in the non-Banach case is an integral transformation that we introduce. This transformation maps continuous Lie algebra-valued curves to smooth ones and leaves the product integral invariant. This transformation is also used to prove a regularity statement in the asymptotic estimate context.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09888-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44535978","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
Geodesics on a K3 surface near the orbifold limit 接近轨道极限的K3表面上的测地线
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-04-03 DOI: 10.1007/s10455-023-09898-w
Jørgen Olsen Lye
{"title":"Geodesics on a K3 surface near the orbifold limit","authors":"Jørgen Olsen Lye","doi":"10.1007/s10455-023-09898-w","DOIUrl":"10.1007/s10455-023-09898-w","url":null,"abstract":"<div><p>This article studies Kummer K3 surfaces close to the orbifold limit. We improve upon estimates for the Calabi–Yau metrics due to Kobayashi. As an application, we study stable closed geodesics. We use the metric estimates to show how there are generally restrictions on the existence of such geodesics. We also show how there can exist stable, closed geodesics in some highly symmetric circumstances due to hyperkähler identities.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-023-09898-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47912407","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
Conformal Bach flow 保形巴赫流
IF 0.7 3区 数学
Annals of Global Analysis and Geometry Pub Date : 2023-03-30 DOI: 10.1007/s10455-023-09897-x
Jiaqi Chen, Peng Lu, Jie Qing
{"title":"Conformal Bach flow","authors":"Jiaqi Chen,&nbsp;Peng Lu,&nbsp;Jie Qing","doi":"10.1007/s10455-023-09897-x","DOIUrl":"10.1007/s10455-023-09897-x","url":null,"abstract":"<div><p>In this article we introduce conformal Bach flow and establish its well-posedness on closed manifolds. We also obtain its backward uniqueness. To give an attempt to study the long-time behavior of conformal Bach flow, assuming that the curvature and the pressure function are bounded, global and local Shi’s type <span>(L^2)</span>-estimate of derivatives of curvatures is derived. Furthermore, using the <span>(L^2)</span>-estimate and based on an idea from (Streets in Calc Var PDE 46:39–54, 2013) we show Shi’s pointwise estimate of derivatives of curvatures without assuming Sobolev constant bound.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44854729","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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