{"title":"论嵌入单元 3 球的零属自由边界极小曲面的面积","authors":"Peter McGrath, Jiahua Zou","doi":"10.1007/s12220-024-01726-2","DOIUrl":null,"url":null,"abstract":"<p>We prove that the area of each nonflat genus zero free boundary minimal surface embedded in the unit 3-ball is less than the area of its radial projection to <span>\\({\\mathbb {S}}^2\\)</span>. The inequality is asymptotically sharp, and we prove any sequence of surfaces saturating it converges weakly to <span>\\({\\mathbb {S}}^2\\)</span>, as currents and as varifolds.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"353 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Areas of Genus Zero Free Boundary Minimal Surfaces Embedded in the Unit 3-Ball\",\"authors\":\"Peter McGrath, Jiahua Zou\",\"doi\":\"10.1007/s12220-024-01726-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove that the area of each nonflat genus zero free boundary minimal surface embedded in the unit 3-ball is less than the area of its radial projection to <span>\\\\({\\\\mathbb {S}}^2\\\\)</span>. The inequality is asymptotically sharp, and we prove any sequence of surfaces saturating it converges weakly to <span>\\\\({\\\\mathbb {S}}^2\\\\)</span>, as currents and as varifolds.</p>\",\"PeriodicalId\":501200,\"journal\":{\"name\":\"The Journal of Geometric Analysis\",\"volume\":\"353 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-06-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Journal of Geometric Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s12220-024-01726-2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Geometric Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s12220-024-01726-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the Areas of Genus Zero Free Boundary Minimal Surfaces Embedded in the Unit 3-Ball
We prove that the area of each nonflat genus zero free boundary minimal surface embedded in the unit 3-ball is less than the area of its radial projection to \({\mathbb {S}}^2\). The inequality is asymptotically sharp, and we prove any sequence of surfaces saturating it converges weakly to \({\mathbb {S}}^2\), as currents and as varifolds.
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