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Global perturbation potential function on complete special holonomy manifolds 完全特殊全息流形上的全局摄动势函数
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2020-05-24 DOI: 10.4310/ajm.2021.v25.n3.a4
Teng Huang
{"title":"Global perturbation potential function on complete special holonomy manifolds","authors":"Teng Huang","doi":"10.4310/ajm.2021.v25.n3.a4","DOIUrl":"https://doi.org/10.4310/ajm.2021.v25.n3.a4","url":null,"abstract":"In this article, we introduce and study the notion of a complete special holonomy manifold $(X,omega)$ which is given by a global perturbation potential function, i.e., there are a function $f$ and a smooth differential $omega'$ on $X$ such that $omega=mathcal{L}_{nabla f}omega+omega'$. We establish some vanishing theorems on the $L^{2}$ harmonic forms under some conditions on the global perturbation potential function.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47126948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 $2$-adic logarithm of units of certain totally imaginary quartic fields 某些全虚四次域单位的$2$进对数
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2020-05-20 DOI: 10.4310/ajm.2021.v25.n2.a1
Jianing Li
{"title":"On the $2$-adic logarithm of units of certain totally imaginary quartic fields","authors":"Jianing Li","doi":"10.4310/ajm.2021.v25.n2.a1","DOIUrl":"https://doi.org/10.4310/ajm.2021.v25.n2.a1","url":null,"abstract":"In this paper, we prove a result on the $2$-adic logarithm of the fundamental unit of the field $mathbb{Q}(sqrt[4]{-q}) $, where $qequiv 3bmod 4$ is a prime. When $qequiv 15bmod 16$, this result confirms a speculation of Coates-Li and has consequences for certain Iwasawa modules arising in their work.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44050870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 4
Bloch’s conjecture for some numerical Campedelli surfaces 一些数值Campedelli曲面的Bloch猜想
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2020-04-01 DOI: 10.4310/ajm.2021.v25.n1.a4
R. Laterveer
{"title":"Bloch’s conjecture for some numerical Campedelli surfaces","authors":"R. Laterveer","doi":"10.4310/ajm.2021.v25.n1.a4","DOIUrl":"https://doi.org/10.4310/ajm.2021.v25.n1.a4","url":null,"abstract":"We prove Bloch's conjecture for numerical Campedelli surfaces with fundamental group of order $9$.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47140031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Higher rho invariant and delocalized eta invariant at infinity 无穷远处的高rho不变量和离域eta不变量
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2020-04-01 DOI: 10.4310/ajm.2022.v26.n2.a5
Xiaoman Chen, Hongzhi Liu, Han Wang, Guoliang Yu
{"title":"Higher rho invariant and delocalized eta invariant at infinity","authors":"Xiaoman Chen, Hongzhi Liu, Han Wang, Guoliang Yu","doi":"10.4310/ajm.2022.v26.n2.a5","DOIUrl":"https://doi.org/10.4310/ajm.2022.v26.n2.a5","url":null,"abstract":"In this paper, we introduce several new secondary invariants for Dirac operators on a complete Riemannian manifold with a uniform positive scalar curvature metric outside a compact set and use these secondary invariants to establish a higher index theorem for the Dirac operators. We apply our theory to study the secondary invariants for a manifold with corner with positive scalar curvature metric on each boundary face.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49341426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Nowhere vanishing primitive of a symplectic form 无处消失的原始辛形式
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2020-03-05 DOI: 10.4310/ajm.2022.v26.n5.a5
B. Stratmann
{"title":"Nowhere vanishing primitive of a symplectic form","authors":"B. Stratmann","doi":"10.4310/ajm.2022.v26.n5.a5","DOIUrl":"https://doi.org/10.4310/ajm.2022.v26.n5.a5","url":null,"abstract":"Let $M$ be a manifold with an exact symplectic form $omega$. Then there is a nowhere vanishing primitive $beta$ for $omega$, i.e. $omega=mathrm{d}beta$.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42905430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Segre’s theorem. An analytic proof of a result in differential geometry 塞格雷定理。微分几何中一个结果的解析证明
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2020-02-09 DOI: 10.4310/ajm.2021.v25.n3.a1
Karl K. Brustad
{"title":"Segre’s theorem. An analytic proof of a result in differential geometry","authors":"Karl K. Brustad","doi":"10.4310/ajm.2021.v25.n3.a1","DOIUrl":"https://doi.org/10.4310/ajm.2021.v25.n3.a1","url":null,"abstract":"We present an analytic approach on how to solve the problem $|nabla u|=f(u)$, $Delta u = g(u)$, in connected domains $Omegasubseteqmathbb{R}^n$.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44027893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 vanishing of the $mu$-invariant for split prime $mathbb{Z}_p$-extensions over imaginary quadratic fields 虚二次域上分割素数$mathbb{Z}_p$-扩展$mu$-不变式的消失
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2020-01-01 DOI: 10.4310/ajm.2020.v24.n2.a5
Vlad-Cristian Crisan, Katharina Müller
{"title":"The vanishing of the $mu$-invariant for split prime $mathbb{Z}_p$-extensions over imaginary quadratic fields","authors":"Vlad-Cristian Crisan, Katharina Müller","doi":"10.4310/ajm.2020.v24.n2.a5","DOIUrl":"https://doi.org/10.4310/ajm.2020.v24.n2.a5","url":null,"abstract":"","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":"24 1","pages":"267-302"},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70391547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 star mean curvature flow on 3-sphere and hyperbolic 3-space 三球和双曲三维空间上的星平均曲率流
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2020-01-01 DOI: 10.4310/ajm.2020.v24.n3.a5
Hsiao-Fan Liu
{"title":"The star mean curvature flow on 3-sphere and hyperbolic 3-space","authors":"Hsiao-Fan Liu","doi":"10.4310/ajm.2020.v24.n3.a5","DOIUrl":"https://doi.org/10.4310/ajm.2020.v24.n3.a5","url":null,"abstract":"","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":"24 1","pages":"483-500"},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70391780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Closed $mathrm{G}_2$-structures with a transitive reductive group of automorphisms 具有传递约化自同构群的闭$ mathm {G}_2$-结构
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2019-11-29 DOI: 10.4310/AJM.2021.v25.n6.a6
F. Podestà, Alberto Raffero
{"title":"Closed $mathrm{G}_2$-structures with a transitive reductive group of automorphisms","authors":"F. Podestà, Alberto Raffero","doi":"10.4310/AJM.2021.v25.n6.a6","DOIUrl":"https://doi.org/10.4310/AJM.2021.v25.n6.a6","url":null,"abstract":". We provide the complete classification of seven-dimensional manifolds endowed with a closed non-parallel G 2 -structure and admitting a transitive reductive group G of automorphisms. In particular, we show that the center of G is one-dimensional and the manifold is the Riemannian product of a flat factor and a non-compact homogeneous six-dimensional manifold endowed with an invariant strictly symplectic half-flat SU(3)-structure.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42635544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 duality of certain GKZ hypergeometric systems 一类GKZ超几何系统的对偶性
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2019-10-09 DOI: 10.4310/ajm.2021.v25.n1.a5
L. Borisov, Z. Han, Chengxi Wang
{"title":"On duality of certain GKZ hypergeometric systems","authors":"L. Borisov, Z. Han, Chengxi Wang","doi":"10.4310/ajm.2021.v25.n1.a5","DOIUrl":"https://doi.org/10.4310/ajm.2021.v25.n1.a5","url":null,"abstract":"We study a pair of conjectures on better behaved GKZ hypergeometric systems of PDEs inspired by Homological mirror symmetry for crepant resolutions of Gorenstein toric singularities. We prove the conjectures in the case of dimension two.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42092575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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