具有常数平均曲率的紧凑嵌入曲面,单位为$\Bbb{S}^2\times\Bbb{{R}$

IF 1.7 1区 数学 Q1 MATHEMATICS
J. M. Manzano, Francisco Torralbo
{"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}
引用次数: 3

摘要

摘要:我们得到了具有常平均曲率$0本文章由计算机程序翻译,如有差异,请以英文原文为准。
分享
查看原文 本刊更多论文
Compact embedded surfaces with constant mean curvature in $\Bbb{S}^2\times\Bbb{R}$
Abstract:We obtain compact orientable embedded surfaces with constant mean curvature $0
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
3.20
自引率
0.00%
发文量
35
审稿时长
24 months
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信