{"title":"具有常数平均曲率的紧凑嵌入曲面,单位为$\\Bbb{S}^2\\times\\Bbb{{R}$","authors":"J. M. Manzano, Francisco Torralbo","doi":"10.1353/ajm.2020.0050","DOIUrl":null,"url":null,"abstract":"Abstract:We obtain compact orientable embedded surfaces with constant mean curvature $0<H<\\{1\\\\over 2\\}$ and arbitrary genus in $\\Bbb\\{S\\}^2\\times\\\\Bbb\\{R\\}$. These surfaces have dihedral symmetry and desingularize a pair of spheres with mean curvature $\\{1\\over 2\\}$ tangent along an equator. This is a particular case of a conjugate Plateau construction of doubly periodic surfaces with constant mean curvature in $\\Bbb\\{S\\}^2\\times\\Bbb\\{R\\}$, $\\Bbb\\{H\\}^2\\times\\\\Bbb\\{R\\}$, and $\\Bbb\\{R\\}^3$ with bounded height and enjoying the symmetries of certain tessellations of $\\Bbb\\{S\\}^2$, $\\Bbb\\{H\\}^2$, and $\\Bbb\\{R\\}^2$ by regular polygons.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2020-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1353/ajm.2020.0050","citationCount":"3","resultStr":"{\"title\":\"Compact embedded surfaces with constant mean curvature in $\\\\Bbb{S}^2\\\\times\\\\Bbb{R}$\",\"authors\":\"J. M. Manzano, Francisco Torralbo\",\"doi\":\"10.1353/ajm.2020.0050\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract:We obtain compact orientable embedded surfaces with constant mean curvature $0<H<\\\\{1\\\\\\\\over 2\\\\}$ and arbitrary genus in $\\\\Bbb\\\\{S\\\\}^2\\\\times\\\\\\\\Bbb\\\\{R\\\\}$. These surfaces have dihedral symmetry and desingularize a pair of spheres with mean curvature $\\\\{1\\\\over 2\\\\}$ tangent along an equator. This is a particular case of a conjugate Plateau construction of doubly periodic surfaces with constant mean curvature in $\\\\Bbb\\\\{S\\\\}^2\\\\times\\\\Bbb\\\\{R\\\\}$, $\\\\Bbb\\\\{H\\\\}^2\\\\times\\\\\\\\Bbb\\\\{R\\\\}$, and $\\\\Bbb\\\\{R\\\\}^3$ with bounded height and enjoying the symmetries of certain tessellations of $\\\\Bbb\\\\{S\\\\}^2$, $\\\\Bbb\\\\{H\\\\}^2$, and $\\\\Bbb\\\\{R\\\\}^2$ by regular polygons.\",\"PeriodicalId\":7453,\"journal\":{\"name\":\"American Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2020-11-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1353/ajm.2020.0050\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"American Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1353/ajm.2020.0050\",\"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":"American Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1353/ajm.2020.0050","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
期刊介绍:
The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.