{"title":"Nonclassical minimizing surfaces with smooth boundary","authors":"Camillo De Lellis, G. Philippis, J. Hirsch","doi":"10.4310/jdg/1669998183","DOIUrl":null,"url":null,"abstract":"We construct a Riemannian metric $g$ on $\\mathbb{R}^4$ (arbitrarily close to the euclidean one) and a smooth simple closed curve $\\Gamma\\subset \\mathbb R^4$ such that the unique area minimizing surface spanned by $\\Gamma$ has infinite topology. Furthermore the metric is almost Kahler and the area minimizing surface is calibrated.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2019-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/jdg/1669998183","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: 6
Abstract
We construct a Riemannian metric $g$ on $\mathbb{R}^4$ (arbitrarily close to the euclidean one) and a smooth simple closed curve $\Gamma\subset \mathbb R^4$ such that the unique area minimizing surface spanned by $\Gamma$ has infinite topology. Furthermore the metric is almost Kahler and the area minimizing surface is calibrated.
期刊介绍:
Publishes the latest research in differential geometry and related areas of differential equations, mathematical physics, algebraic geometry, and geometric topology.