$mathbb{R}^4$中的最小分片线性锥体

Pub Date : 2024-02-26 DOI:10.7146/math.scand.a-140336

Asgeir Valfells

{"title":"$mathbb{R}^4$中的最小分片线性锥体","authors":"Asgeir Valfells","doi":"10.7146/math.scand.a-140336","DOIUrl":null,"url":null,"abstract":"We consider three dimensional piecewise linear cones in $\\mathbb{R}^4$ that are mass minimal with respect to Lipschitz maps in the sense of [Almgren, F., Mem. Amer. Math. Soc. 4 (1976), no. 165] as in [Taylor, J. E., Ann. of Math. (2) 103 (1976), no. 3, 489–539]. There are three that arise naturally by taking products of $\\mathbb{R}$ with lower dimensional cases and earlier literature has demonstrated the existence of two with 0-dimensional singularities. We classify all possible candidates and demonstrate that there are no piecewise linear minimizers outside these five.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Minimal piecewise linear cones in $\\\\mathbb{R}^4$\",\"authors\":\"Asgeir Valfells\",\"doi\":\"10.7146/math.scand.a-140336\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider three dimensional piecewise linear cones in $\\\\mathbb{R}^4$ that are mass minimal with respect to Lipschitz maps in the sense of [Almgren, F., Mem. Amer. Math. Soc. 4 (1976), no. 165] as in [Taylor, J. E., Ann. of Math. (2) 103 (1976), no. 3, 489–539]. There are three that arise naturally by taking products of $\\\\mathbb{R}$ with lower dimensional cases and earlier literature has demonstrated the existence of two with 0-dimensional singularities. We classify all possible candidates and demonstrate that there are no piecewise linear minimizers outside these five.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-02-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.7146/math.scand.a-140336\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7146/math.scand.a-140336","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们考虑$\mathbb{R}^4$中的三维片断线性锥，这些锥在[Almgren, F., Mem. Amer. Math. Soc. 4 (1976), no. 165]意义上相对于Lipschitz映射是质量最小的，如[Taylor, J. E., Ann. of Math. (2) 103 (1976), no. 3, 489-539]。有三个是通过$\mathbb{R}$ 与低维情况的乘积自然产生的，早先的文献已经证明了两个 0 维奇点的存在。我们对所有可能的候选方案进行了分类，并证明在这五个方案之外不存在片断线性最小值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

Minimal piecewise linear cones in $\mathbb{R}^4$

We consider three dimensional piecewise linear cones in $\mathbb{R}^4$ that are mass minimal with respect to Lipschitz maps in the sense of [Almgren, F., Mem. Amer. Math. Soc. 4 (1976), no. 165] as in [Taylor, J. E., Ann. of Math. (2) 103 (1976), no. 3, 489–539]. There are three that arise naturally by taking products of $\mathbb{R}$ with lower dimensional cases and earlier literature has demonstrated the existence of two with 0-dimensional singularities. We classify all possible candidates and demonstrate that there are no piecewise linear minimizers outside these five.

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