{"title":"混合锥尖奇异度量空间的l2 - poincar<s:1> - dolbeault引理","authors":"Junchao Shentu, Chen Zhao","doi":"10.1142/s1793525321500473","DOIUrl":null,"url":null,"abstract":"The existence of Kähler Einstein metrics with mixed cone and cusp singularity has received considerable attentions in recent years. It is believed that such kind of metric would give rise to important geometric invariants. We computed their [Formula: see text]-Hodge–Frölicher spectral sequence under the Dirichlet and Neumann boundary conditions and examine the pure Hodge structures on them. It turns out that these cohomologies agree well with the de Rham cohomology of a good compactification.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An L2-Poincaré–Dolbeault lemma of spaces with mixed cone-cusp singular metrics\",\"authors\":\"Junchao Shentu, Chen Zhao\",\"doi\":\"10.1142/s1793525321500473\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The existence of Kähler Einstein metrics with mixed cone and cusp singularity has received considerable attentions in recent years. It is believed that such kind of metric would give rise to important geometric invariants. We computed their [Formula: see text]-Hodge–Frölicher spectral sequence under the Dirichlet and Neumann boundary conditions and examine the pure Hodge structures on them. It turns out that these cohomologies agree well with the de Rham cohomology of a good compactification.\",\"PeriodicalId\":49151,\"journal\":{\"name\":\"Journal of Topology and Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-09-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Topology and Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s1793525321500473\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology and Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1793525321500473","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
An L2-Poincaré–Dolbeault lemma of spaces with mixed cone-cusp singular metrics
The existence of Kähler Einstein metrics with mixed cone and cusp singularity has received considerable attentions in recent years. It is believed that such kind of metric would give rise to important geometric invariants. We computed their [Formula: see text]-Hodge–Frölicher spectral sequence under the Dirichlet and Neumann boundary conditions and examine the pure Hodge structures on them. It turns out that these cohomologies agree well with the de Rham cohomology of a good compactification.
期刊介绍：
This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
