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Conformal vector fields and σk-scalarcurvatures 共形向量场与σk-标度循环
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2022-04-06 DOI: 10.2140/pjm.2022.316.453
Xingwang Xu, J. Ye
{"title":"Conformal vector fields and σk-scalar\u0000curvatures","authors":"Xingwang Xu, J. Ye","doi":"10.2140/pjm.2022.316.453","DOIUrl":"https://doi.org/10.2140/pjm.2022.316.453","url":null,"abstract":"","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45745193","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
The second best constant for the Hardy–Sobolevinequality on manifolds 流形上hardy - sobolev不等式的次优常数
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2022-04-06 DOI: 10.2140/pjm.2022.316.249
Hussein Cheikh Ali
{"title":"The second best constant for the Hardy–Sobolev\u0000inequality on manifolds","authors":"Hussein Cheikh Ali","doi":"10.2140/pjm.2022.316.249","DOIUrl":"https://doi.org/10.2140/pjm.2022.316.249","url":null,"abstract":"We consider the second best constant in the Hardy-Sobolev inequality on a Riemannian manifold. More precisely, we are interested with the existence of extremal functions for this inequality. This problem was tackled by Djadli-Druet [5] for Sobolev inequalities. Here, we establish the corresponding result for the singular case. In addition, we perform a blow-up analysis of solutions Hardy-Sobolev equations of minimizing type. This yields informations on the value of the second best constant in the related Riemannian functional inequality.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45179232","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
A symplectic form on the space of embedded symplectic surfaces and its reduction by reparametrizations 嵌入辛曲面空间上的辛形式及其再参数化化
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2022-04-06 DOI: 10.2140/pjm.2022.316.409
Liat Kessler
{"title":"A symplectic form on the space of embedded symplectic surfaces and its reduction by reparametrizations","authors":"Liat Kessler","doi":"10.2140/pjm.2022.316.409","DOIUrl":"https://doi.org/10.2140/pjm.2022.316.409","url":null,"abstract":"","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48326902","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
No periodic geodesics in jet space 射流空间中没有周期性测地线
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2022-03-30 DOI: 10.2140/pjm.2023.322.11
Alejandro Bravo-Doddoli
{"title":"No periodic geodesics in jet space","authors":"Alejandro Bravo-Doddoli","doi":"10.2140/pjm.2023.322.11","DOIUrl":"https://doi.org/10.2140/pjm.2023.322.11","url":null,"abstract":"The $J^k$ space of $k$-jets of a real function of one real variable $x$ admits the structure of a sub-Riemannian manifold, which then has an associated Hamiltonian geodesic flow, and it is integrable. As in any Hamiltonian flow, a natural question is the existence of periodic solutions. Does $J^k$ have periodic geodesics? This study will find the action-angle coordinates in $T^*J^k$ for the geodesic flow and demonstrate that geodesics in $J^k$ are never periodic.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43587428","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
The Fox–Hatcher cycle and a Vassiliev invariantof order three Fox-Hatcher循环和一个三阶Vassiliev不变量
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2022-03-29 DOI: 10.2140/pjm.2023.323.281
Saki Kanou, K. Sakai
{"title":"The Fox–Hatcher cycle and a Vassiliev invariant\u0000of order three","authors":"Saki Kanou, K. Sakai","doi":"10.2140/pjm.2023.323.281","DOIUrl":"https://doi.org/10.2140/pjm.2023.323.281","url":null,"abstract":"We show that the integration of a 1-cocycle I(X) of the space of long knots in R^3 over the Fox-Hatcher 1-cycles gives rise to a Vassiliev invariant of order exactly three. This result can be seen as a continuation of the previous work of the second named author, proving that the integration of I(X) over the Gramain 1-cycles is the Casson invariant, the unique nontrivial Vassiliev invariant of order two (up to scalar multiplications). The result in the present paper is also analogous to part of Mortier's result. Our result differs from, but is motivated by, Mortier's one in that the 1-cocycle I(X) is given by the configuration space integrals associated with graphs while Mortier's cocycle is obtained in a combinatorial way.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49550335","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 geometry and topology of stationary multiaxisymmetric vacuum black holes in higher dimensions 高维定常多轴对称真空黑洞的几何和拓扑
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2022-03-16 DOI: 10.2140/pjm.2023.322.59
Vishnu Kakkat, M. Khuri, Jordan Rainone, G. Weinstein
{"title":"The geometry and topology of stationary multiaxisymmetric vacuum black holes in higher dimensions","authors":"Vishnu Kakkat, M. Khuri, Jordan Rainone, G. Weinstein","doi":"10.2140/pjm.2023.322.59","DOIUrl":"https://doi.org/10.2140/pjm.2023.322.59","url":null,"abstract":"Extending recent work in 5 dimensions, we prove the existence and uniqueness of solutions to the reduced Einstein equations for vacuum black holes in $(n+3)$-dimensional spacetimes admitting the isometry group $mathbb{R}times U(1)^{n}$, with Kaluza-Klein asymptotics for $ngeq3$. This is equivalent to establishing existence and uniqueness for singular harmonic maps $varphi: mathbb{R}^3setminusGammarightarrow SL(n+1,mathbb{R})/SO(n+1)$ with prescribed blow-up along $Gamma$, a subset of the $z$-axis in $mathbb{R}^3$. We also analyze the topology of the domain of outer communication for these spacetimes, by developing an appropriate generalization of the plumbing construction used in the lower dimensional case. Furthermore, we provide a counterexample to a conjecture of Hollands-Ishibashi concerning the topological classification of the domain of outer communication. A refined version of the conjecture is then presented and established in spacetime dimensions less than 8.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49397659","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: 3
An isoperimetric inequality of minimal hypersurfaces in spheres 球面上极小超曲面的等周不等式
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2022-03-13 DOI: 10.2140/pjm.2023.324.143
Fagui Li, Niang-Shin Chen
{"title":"An isoperimetric inequality of minimal hypersurfaces in spheres","authors":"Fagui Li, Niang-Shin Chen","doi":"10.2140/pjm.2023.324.143","DOIUrl":"https://doi.org/10.2140/pjm.2023.324.143","url":null,"abstract":"Let $ M^n$ be a closed immersed minimal hypersurface in the unit sphere $mathbb{S}^{n+1}$. We establish a special isoperimetric inequality of $M^n$. As an application, if the scalar curvature of $ M^n$ is constant, then we get a uniform lower bound independent of $M^n$ for the isoperimetric inequality. In addition, we obtain an inequality between Cheeger's isoperimetric constant and the volume of the nodal set of the height function.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44275738","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
Compactness of conformal metrics with integral bounds on Ricci curvature 里奇曲率上有积分界的共形度量的紧性
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2022-02-26 DOI: 10.2140/pjm.2022.316.65
Conghan Dong, Yuxiang Li
{"title":"Compactness of conformal metrics with integral bounds on Ricci curvature","authors":"Conghan Dong, Yuxiang Li","doi":"10.2140/pjm.2022.316.65","DOIUrl":"https://doi.org/10.2140/pjm.2022.316.65","url":null,"abstract":"","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46114660","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 CR morphisms CR态射的刚性
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2022-02-26 DOI: 10.2140/pjm.2022.316.207
Xiankui Meng, S. Yau
{"title":"Rigidity of CR morphisms","authors":"Xiankui Meng, S. Yau","doi":"10.2140/pjm.2022.316.207","DOIUrl":"https://doi.org/10.2140/pjm.2022.316.207","url":null,"abstract":"","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49586173","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
Derived right adjoints of parabolic induction: an example 抛物型归纳的导出右邻接：一个例子
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2022-02-20 DOI: 10.2140/pjm.2022.321.345
K. Kozioł
{"title":"Derived right adjoints of parabolic induction: an example","authors":"K. Kozioł","doi":"10.2140/pjm.2022.321.345","DOIUrl":"https://doi.org/10.2140/pjm.2022.321.345","url":null,"abstract":"Suppose $p geq 5$ is a prime number, and let $G = textrm{SL}_2(mathbb{Q}_p)$. We calculate the derived functors $textrm{R}^nmathcal{R}_B^G(pi)$, where $B$ is a Borel subgroup of $G$, $mathcal{R}_B^G$ is the right adjoint of smooth parabolic induction constructed by Vign'eras, and $pi$ is any smooth, absolutely irreducible, mod $p$ representation of $G$.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45389075","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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