{"title":"最大体积增长的Calabi-Yau流形上的次二次调和函数","authors":"Shih-Kai Chiu","doi":"10.1002/cpa.22182","DOIUrl":null,"url":null,"abstract":"<p>On a complete Calabi-Yau manifold <span></span><math>\n <semantics>\n <mi>M</mi>\n <annotation>$M$</annotation>\n </semantics></math> with maximal volume growth, a harmonic function with subquadratic polynomial growth is the real part of a holomorphic function. This generalizes a result of Conlon-Hein. We prove this result by proving a Liouville-type theorem for harmonic 1-forms, which follows from a new local <span></span><math>\n <semantics>\n <msup>\n <mi>L</mi>\n <mn>2</mn>\n </msup>\n <annotation>$L^2$</annotation>\n </semantics></math> estimate of the exterior derivative.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"77 6","pages":"3080-3106"},"PeriodicalIF":3.1000,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22182","citationCount":"0","resultStr":"{\"title\":\"Subquadratic harmonic functions on Calabi-Yau manifolds with maximal volume growth\",\"authors\":\"Shih-Kai Chiu\",\"doi\":\"10.1002/cpa.22182\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>On a complete Calabi-Yau manifold <span></span><math>\\n <semantics>\\n <mi>M</mi>\\n <annotation>$M$</annotation>\\n </semantics></math> with maximal volume growth, a harmonic function with subquadratic polynomial growth is the real part of a holomorphic function. This generalizes a result of Conlon-Hein. We prove this result by proving a Liouville-type theorem for harmonic 1-forms, which follows from a new local <span></span><math>\\n <semantics>\\n <msup>\\n <mi>L</mi>\\n <mn>2</mn>\\n </msup>\\n <annotation>$L^2$</annotation>\\n </semantics></math> estimate of the exterior derivative.</p>\",\"PeriodicalId\":10601,\"journal\":{\"name\":\"Communications on Pure and Applied Mathematics\",\"volume\":\"77 6\",\"pages\":\"3080-3106\"},\"PeriodicalIF\":3.1000,\"publicationDate\":\"2023-11-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22182\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications on Pure and Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/cpa.22182\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications on Pure and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/cpa.22182","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Subquadratic harmonic functions on Calabi-Yau manifolds with maximal volume growth
On a complete Calabi-Yau manifold with maximal volume growth, a harmonic function with subquadratic polynomial growth is the real part of a holomorphic function. This generalizes a result of Conlon-Hein. We prove this result by proving a Liouville-type theorem for harmonic 1-forms, which follows from a new local estimate of the exterior derivative.
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
