{"title":"Kähler流形和极限空间的全纯平分曲率的比较几何","authors":"J. Lott","doi":"10.1215/00127094-2021-0058","DOIUrl":null,"url":null,"abstract":"We give an analog of triangle comparison for Kaehler manifolds with a lower bound on the holomorphic bisectional curvature. We show that the condition passes to noncollapsed Gromov-Hausdorff limits. We discuss tangent cones and singular Kaehler spaces.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2020-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Comparison geometry of holomorphic bisectional curvature for Kähler manifolds and limit spaces\",\"authors\":\"J. Lott\",\"doi\":\"10.1215/00127094-2021-0058\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give an analog of triangle comparison for Kaehler manifolds with a lower bound on the holomorphic bisectional curvature. We show that the condition passes to noncollapsed Gromov-Hausdorff limits. We discuss tangent cones and singular Kaehler spaces.\",\"PeriodicalId\":11447,\"journal\":{\"name\":\"Duke Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2020-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Duke Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1215/00127094-2021-0058\",\"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":"Duke Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1215/00127094-2021-0058","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Comparison geometry of holomorphic bisectional curvature for Kähler manifolds and limit spaces
We give an analog of triangle comparison for Kaehler manifolds with a lower bound on the holomorphic bisectional curvature. We show that the condition passes to noncollapsed Gromov-Hausdorff limits. We discuss tangent cones and singular Kaehler spaces.
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