{"title":"里奇曲率、体积凸性和最小拉格朗日子平面","authors":"Tommaso Pacini","doi":"10.4310/jsg.2023.v21.n6.a3","DOIUrl":null,"url":null,"abstract":"We show that, in toric Kähler geometry, the sign of the Ricci curvature corresponds exactly to convexity properties of the volume functional.We also discuss analogous relationships in the more general context of quasi-homogeneous manifolds, and existence results for minimal Lagrangian submanifolds.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Ricci curvature, the convexity of volume and minimal Lagrangian submanifolds\",\"authors\":\"Tommaso Pacini\",\"doi\":\"10.4310/jsg.2023.v21.n6.a3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that, in toric Kähler geometry, the sign of the Ricci curvature corresponds exactly to convexity properties of the volume functional.We also discuss analogous relationships in the more general context of quasi-homogeneous manifolds, and existence results for minimal Lagrangian submanifolds.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-06-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/jsg.2023.v21.n6.a3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/jsg.2023.v21.n6.a3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Ricci curvature, the convexity of volume and minimal Lagrangian submanifolds
We show that, in toric Kähler geometry, the sign of the Ricci curvature corresponds exactly to convexity properties of the volume functional.We also discuss analogous relationships in the more general context of quasi-homogeneous manifolds, and existence results for minimal Lagrangian submanifolds.
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