{"title":"Minimal Surfaces in $\\mathbb{H}_2\\times \\mathbb{R}$: Nonfillable Curves","authors":"Baris Coskunuzer","doi":"10.1142/S1793525321500230","DOIUrl":null,"url":null,"abstract":"We study the asymptotic Plateau problem in $\\mathbb{H}_2\\times \\mathbb{R}$. We give the first examples of non-fillable finite curves with no thin tail in the asymptotic cylinder. Furthermore, we study the fillability question for infinite curves in the asymptotic boundary.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"9 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/S1793525321500230","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
We study the asymptotic Plateau problem in $\mathbb{H}_2\times \mathbb{R}$. We give the first examples of non-fillable finite curves with no thin tail in the asymptotic cylinder. Furthermore, we study the fillability question for infinite curves in the asymptotic boundary.
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