中规范球的一个特征ℍ n通过水平曲率

IF 1.3 3区数学 Q1 MATHEMATICS

Advances in Calculus of Variations Pub Date : 2023-03-31 DOI:10.1515/acv-2022-0058

Chiara Guidi, Vittorio Martino, G. Tralli

{"title":"中规范球的一个特征ℍ n通过水平曲率","authors":"Chiara Guidi, Vittorio Martino, G. Tralli","doi":"10.1515/acv-2022-0058","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we aim at identifying the level sets of the gauge norm in the Heisenberg group ℍ n {{\\mathbb{H}^{n}}} via the prescription of their (non-constant) horizontal mean curvature. We establish a uniqueness result in ℍ 1 {\\mathbb{H}^{1}} under an assumption on the location of the singular set, and in ℍ n {\\mathbb{H}^{n}} for n ≥ 2 {n\\geq 2} in the proper class of horizontally umbilical hypersurfaces.","PeriodicalId":49276,"journal":{"name":"Advances in Calculus of Variations","volume":" ","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A characterization of gauge balls in ℍ n by horizontal curvature\",\"authors\":\"Chiara Guidi, Vittorio Martino, G. Tralli\",\"doi\":\"10.1515/acv-2022-0058\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, we aim at identifying the level sets of the gauge norm in the Heisenberg group ℍ n {{\\\\mathbb{H}^{n}}} via the prescription of their (non-constant) horizontal mean curvature. We establish a uniqueness result in ℍ 1 {\\\\mathbb{H}^{1}} under an assumption on the location of the singular set, and in ℍ n {\\\\mathbb{H}^{n}} for n ≥ 2 {n\\\\geq 2} in the proper class of horizontally umbilical hypersurfaces.\",\"PeriodicalId\":49276,\"journal\":{\"name\":\"Advances in Calculus of Variations\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-03-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Calculus of Variations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/acv-2022-0058\",\"RegionNum\":3,\"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":"Advances in Calculus of Variations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/acv-2022-0058","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 2

摘要

摘要在本文中，我们旨在识别Heisenberg群中规范范数的水平集ℍ n｛\mathbb｛H｝^｛n｝｝｝｝通过它们的（非常数）水平平均曲率的规定。我们在ℍ 1｛\mathbb｛H｝^｛1｝｝在关于奇异集位置的假设下ℍ n｛\mathbb｛H｝^｛n｝｝对于n≥2｛n\geq2｝在适当的水平脐超曲面类中。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A characterization of gauge balls in ℍ n by horizontal curvature

Abstract In this paper, we aim at identifying the level sets of the gauge norm in the Heisenberg group ℍ n {{\mathbb{H}^{n}}} via the prescription of their (non-constant) horizontal mean curvature. We establish a uniqueness result in ℍ 1 {\mathbb{H}^{1}} under an assumption on the location of the singular set, and in ℍ n {\mathbb{H}^{n}} for n ≥ 2 {n\geq 2} in the proper class of horizontally umbilical hypersurfaces.

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

Advances in Calculus of Variations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.90

自引率

5.90%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Calculus of Variations publishes high quality original research focusing on that part of calculus of variation and related applications which combines tools and methods from partial differential equations with geometrical techniques.