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Circular spherical divisors and their contact topology 圆球形除法及其接触拓扑学
IF 0.7 4区 数学
Communications in Analysis and Geometry Pub Date : 2024-07-29 DOI: 10.4310/cag.2023.v31.n10.a2
Li,Tian-Jun, Mak,Cheuk Yu, Min,Jie
{"title":"Circular spherical divisors and their contact topology","authors":"Li,Tian-Jun, Mak,Cheuk Yu, Min,Jie","doi":"10.4310/cag.2023.v31.n10.a2","DOIUrl":"https://doi.org/10.4310/cag.2023.v31.n10.a2","url":null,"abstract":"This paper investigates the symplectic and contact topology associated to circular spherical divisors. We classify, up to toric equivalence, all concave circular spherical divisors $ D $ that can be embedded symplectically into a closed symplectic 4-manifold and show they are all realized as symplectic log Calabi-Yau pairs if their complements are minimal. We then determine the Stein fillability and rational homology type of all minimal symplectic fillings for the boundary torus bundles of such $D$. When $ D $ is anticanonical and convex, we give explicit Betti number bounds for Stein fillings of its boundary contact torus bundle.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141863781","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
Kodaira dimension & the Yamabe problem, II 小平维度与山边问题 II
IF 0.7 4区 数学
Communications in Analysis and Geometry Pub Date : 2024-07-29 DOI: 10.4310/cag.2023.v31.n10.a4
Albanese,Michael, LeBrun,Claude
{"title":"Kodaira dimension & the Yamabe problem, II","authors":"Albanese,Michael, LeBrun,Claude","doi":"10.4310/cag.2023.v31.n10.a4","DOIUrl":"https://doi.org/10.4310/cag.2023.v31.n10.a4","url":null,"abstract":"For compact complex surfaces $(M^{4}, J)$ of Kähler type, it was previously shown [30] that the sign of the Yamabe invariant $mathscr{Y}(M)$ only depends on the Kodaira dimension $text{Kod} (M, J)$. In this paper, we prove that this pattern in fact extends to all compact complex surfaces except those of class VII. In the process, we also reprove a result from [2] that explains why the exclusion of class VII is essential here.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141863785","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
Filling links and spines in 3-manifolds 三芒星中的填充链接和棘刺
IF 0.7 4区 数学
Communications in Analysis and Geometry Pub Date : 2024-07-29 DOI: 10.4310/cag.2023.v31.n10.a1
Freedman,Michael, Krushkal,Vyacheslav, Leininger,Christopher J., Reid,Alan W.
{"title":"Filling links and spines in 3-manifolds","authors":"Freedman,Michael, Krushkal,Vyacheslav, Leininger,Christopher J., Reid,Alan W.","doi":"10.4310/cag.2023.v31.n10.a1","DOIUrl":"https://doi.org/10.4310/cag.2023.v31.n10.a1","url":null,"abstract":"We introduce and study the notion of filling links in $3$-manifolds: a link $L$ is filling in $M$ if for any $1$-spine $G$ of $M$ which is disjoint from $L$, $pi _{1}(G)$ injects into $pi _{1}(Msmallsetminus L)$. A weaker \"$k$-filling\" version concerns injectivity modulo $k$-th term of the lower central series. For each $kgeq 2$ we construct a $k$-filling link in the $3$-torus. The proof relies on an extension of the Stallings theorem which may be of independent interest. We discuss notions related to \"filling\" links in $3$-manifolds, and formulate several open problems. The appendix by C. Leininger and A. Reid establishes the existence of a filling hyperbolic link in any closed orientable $3$-manifold with $pi _{1}(M)$ of rank $2$.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141863780","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 Dirichlet principle for the complex $k$-Hessian functional 复$k$-Hessian函数的狄利克特原理
IF 0.7 4区 数学
Communications in Analysis and Geometry Pub Date : 2024-07-29 DOI: 10.4310/cag.2023.v31.n10.a7
Wang,Yi, Xu,Hang
{"title":"The Dirichlet principle for the complex $k$-Hessian functional","authors":"Wang,Yi, Xu,Hang","doi":"10.4310/cag.2023.v31.n10.a7","DOIUrl":"https://doi.org/10.4310/cag.2023.v31.n10.a7","url":null,"abstract":"We study the variational structure of the complex $k$-Hessian equation on bounded domain $Xsubset mathbb C^{n}$ with boundary $M=partial X$. We prove that the Dirichlet problem $sigma _{k} (partial bar{partial} u) =0$ in $X$, and $u=f$ on $M$ is variational and we give an explicit construction of the associated functional $ mathcal{E}_{k}(u)$. Moreover we prove $ mathcal{E}_{k}(u)$ satisfies the Dirichlet principle. In a special case when $k=2$, our constructed functional $ mathcal{E}_{2}(u)$ involves the Hermitian mean curvature of the boundary, the notion first introduced and studied by X. Wang [37]. Earlier work of J. Case and and the first author of this article [9] introduced a boundary operator for the (real) $k$-Hessian functional which satisfies the Dirichlet principle. The present paper shows that there is a parallel picture in the complex setting.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141863786","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
Weighted $L^{2}$ estimates for $overline{partial }$ and the Corona problem of several complex variables $overline{partial}$的加权$L^{2}$估计值和多个复杂变量的日冕问题
IF 0.7 4区 数学
Communications in Analysis and Geometry Pub Date : 2024-07-29 DOI: 10.4310/cag.2023.v31.n10.a3
Li,Song-Ying
{"title":"Weighted $L^{2}$ estimates for $overline{partial }$ and the Corona problem of several complex variables","authors":"Li,Song-Ying","doi":"10.4310/cag.2023.v31.n10.a3","DOIUrl":"https://doi.org/10.4310/cag.2023.v31.n10.a3","url":null,"abstract":"In the paper, we apply Hörmander's weighted $L^{2}$ estimate for $overline{partial }$ to study the Corona problem on the unit ball $B_{n}$ in ${mathbf{C}}^{n}$. We introduce a new holomorphic function space ${mathcal S}(B_{n})$ which is slightly small than $H^{infty}(B_{n})$. We can solve the Corona problems on ${mathcal S}(B_{n})$ instead of $H^{infty}(B_{n})$. We also provide a new proof of $H^{infty }cdot BMOA$ solution for the Corona problem which was first obtained by Varopoulos [41].","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141863782","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
Bergman-Einstein metric on a Stein space with a strongly pseudoconvex boundary 具有强伪凸边界的斯泰因空间上的伯格曼-爱因斯坦度量
IF 0.7 4区 数学
Communications in Analysis and Geometry Pub Date : 2024-07-26 DOI: 10.4310/cag.2023.v31.n7.a3
Huang,Xiaojun, Li,Xiaoshan
{"title":"Bergman-Einstein metric on a Stein space with a strongly pseudoconvex boundary","authors":"Huang,Xiaojun, Li,Xiaoshan","doi":"10.4310/cag.2023.v31.n7.a3","DOIUrl":"https://doi.org/10.4310/cag.2023.v31.n7.a3","url":null,"abstract":"Let $Omega $ be a Stein space with a compact smooth strongly pseudoconvex boundary. We prove that the boundary is spherical if its Bergman metric over $text{Reg}(Omega )$ is Kähler-Einstein.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780471","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
Analysis of Type I singularities in the harmonic Ricci flow 谐波利玛窦流中的 I 型奇点分析
IF 0.7 4区 数学
Communications in Analysis and Geometry Pub Date : 2024-07-26 DOI: 10.4310/cag.2023.v31.n7.a6
Di Matteo,Gianmichele
{"title":"Analysis of Type I singularities in the harmonic Ricci flow","authors":"Di Matteo,Gianmichele","doi":"10.4310/cag.2023.v31.n7.a6","DOIUrl":"https://doi.org/10.4310/cag.2023.v31.n7.a6","url":null,"abstract":"In [8], Enders, Müller and Topping showed that any blow up sequence of a Type I Ricci flow near a singular point converges to a non-trivial gradient Ricci soliton, leading them to conclude that for such flows all reasonable definitions of singular points agree with each other. We prove the analogous result for the harmonic Ricci flow, generalizing in particular results of Guo, Huang and Phong [11] and Shi [25]. In order to obtain our result, we develop refined compactness theorems, a new pseudolocality theorem, and a notion of reduced length and volume based at the singular time for the harmonic Ricci flow.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780473","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
Mass of asymptotically flat 3-manifolds with boundary 有边界的渐近平坦三漫游体的质量
IF 0.7 4区 数学
Communications in Analysis and Geometry Pub Date : 2024-07-26 DOI: 10.4310/cag.2023.v31.n7.a1
Hirsch,Sven, Miao,Pengzi, Tsang,Tin-Yau
{"title":"Mass of asymptotically flat 3-manifolds with boundary","authors":"Hirsch,Sven, Miao,Pengzi, Tsang,Tin-Yau","doi":"10.4310/cag.2023.v31.n7.a1","DOIUrl":"https://doi.org/10.4310/cag.2023.v31.n7.a1","url":null,"abstract":"We study the mass of asymptotically flat $3$-manifolds with boundary using the method of Bray-Kazaras-Khuri-Stern cite{BKKS}. More precisely, we derive a mass formula on the union of an asymptotically flat manifold and fill-ins of its boundary, and give new sufficient conditions guaranteeing the positivity of the mass. Motivation to such consideration comes from studying the quasi-local mass of the boundary surface. If the boundary isometrically embeds in the Euclidean space, we apply the formula to obtain convergence of the Brown-York mass along large surfaces tending to $infty$ which include the scaling of any fixed coordinate-convex surface.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780469","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
Hamilton type entropy formula along the Ricci flow on surfaces with boundary 有边界曲面上沿利玛窦流的汉密尔顿式熵公式
IF 0.7 4区 数学
Communications in Analysis and Geometry Pub Date : 2024-07-26 DOI: 10.4310/cag.2023.v31.n7.a2
Kunikawa,Keita, Sakurai,Yohei
{"title":"Hamilton type entropy formula along the Ricci flow on surfaces with boundary","authors":"Kunikawa,Keita, Sakurai,Yohei","doi":"10.4310/cag.2023.v31.n7.a2","DOIUrl":"https://doi.org/10.4310/cag.2023.v31.n7.a2","url":null,"abstract":"In this article, we establish a monotonicity formula of Hamilton type entropy along Ricci flow on compact surfaces with boundary. We also study the relation between our entropy functional and the $mathcal{W}$-functional of Perelman type.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780470","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
Singular hyperbolic metrics and negative subharmonic functions 奇异双曲度量和负次谐函数
IF 0.7 4区 数学
Communications in Analysis and Geometry Pub Date : 2024-07-26 DOI: 10.4310/cag.2023.v31.n7.a7
Feng,Yu, Shi,Yiqian, Song,Jijian, Xu,Bin
{"title":"Singular hyperbolic metrics and negative subharmonic functions","authors":"Feng,Yu, Shi,Yiqian, Song,Jijian, Xu,Bin","doi":"10.4310/cag.2023.v31.n7.a7","DOIUrl":"https://doi.org/10.4310/cag.2023.v31.n7.a7","url":null,"abstract":"We propose a conjecture that the monodromy group of a singular hyperbolic metric on a non-hyperbolic Riemann surface is Zariski dense in $text{PSL}(2,,{mathbb R})$. By using meromorphic differentials and affine connections, we obtain evidence of the conjecture that the monodromy group of the singular hyperbolic metric cannot be contained in four classes of one-dimensional Lie subgroups of $text{PSL}(2,,{mathbb R})$. Moreover, we confirm the conjecture if the Riemann surface is the once punctured Riemann sphere, the twice punctured Riemann sphere, a once punctured torus or a compact Riemann surface.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780476","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
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