{"title":"有限总曲率零属完全极小曲面的高斯图像","authors":"Yu Kawakami, Mototsugu Watanabe","doi":"10.1007/s12220-024-01721-7","DOIUrl":null,"url":null,"abstract":"<p>This paper aims to present a systematic study on the Gauss images of complete minimal surfaces of genus 0 of finite total curvature in Euclidean 3-space and Euclidean 4-space. We focus on the number of omitted values and the total weight of the totally ramified values of their Gauss maps. In particular, we construct new complete minimal surfaces of finite total curvature whose Gauss maps have 2 omitted values and 1 totally ramified value of order 2, that is, the total weight of the totally ramified values of their Gauss maps are <span>\\(5/2\\,(=2.5)\\)</span> in Euclidean 3-space and Euclidean 4-space, respectively. Moreover we discuss several outstanding problems in this study.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"190 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Gauss Images of Complete Minimal Surfaces of Genus Zero of Finite Total Curvature\",\"authors\":\"Yu Kawakami, Mototsugu Watanabe\",\"doi\":\"10.1007/s12220-024-01721-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper aims to present a systematic study on the Gauss images of complete minimal surfaces of genus 0 of finite total curvature in Euclidean 3-space and Euclidean 4-space. We focus on the number of omitted values and the total weight of the totally ramified values of their Gauss maps. In particular, we construct new complete minimal surfaces of finite total curvature whose Gauss maps have 2 omitted values and 1 totally ramified value of order 2, that is, the total weight of the totally ramified values of their Gauss maps are <span>\\\\(5/2\\\\,(=2.5)\\\\)</span> in Euclidean 3-space and Euclidean 4-space, respectively. Moreover we discuss several outstanding problems in this study.</p>\",\"PeriodicalId\":501200,\"journal\":{\"name\":\"The Journal of Geometric Analysis\",\"volume\":\"190 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-06-25\",\"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/s12220-024-01721-7\",\"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/s12220-024-01721-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Gauss Images of Complete Minimal Surfaces of Genus Zero of Finite Total Curvature
This paper aims to present a systematic study on the Gauss images of complete minimal surfaces of genus 0 of finite total curvature in Euclidean 3-space and Euclidean 4-space. We focus on the number of omitted values and the total weight of the totally ramified values of their Gauss maps. In particular, we construct new complete minimal surfaces of finite total curvature whose Gauss maps have 2 omitted values and 1 totally ramified value of order 2, that is, the total weight of the totally ramified values of their Gauss maps are \(5/2\,(=2.5)\) in Euclidean 3-space and Euclidean 4-space, respectively. Moreover we discuss several outstanding problems in this study.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
