{"title":"A stability result for translating spacelike graphs in Lorentz manifolds","authors":"","doi":"10.1007/s10473-024-0206-z","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, we investigate spacelike graphs defined over a domain Ω ⊂ <em>M</em><sup><em>n</em></sup> in the Lorentz manifold <em>M</em><sup><em>n</em></sup> × ℝ with the metric −d<em>s</em><sup>2</sup> + <em>σ</em>, where <em>M</em><sup><em>n</em></sup> is a complete Riemannian <em>n</em>-manifold with the metric σ, Ω has piecewise smooth boundary, and ℝ denotes the Euclidean 1-space. We prove an interesting stability result for translating spacelike graphs in <em>M</em><sup><em>n</em></sup> × ℝ under a conformal transformation.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Scientia","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10473-024-0206-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we investigate spacelike graphs defined over a domain Ω ⊂ Mn in the Lorentz manifold Mn × ℝ with the metric −ds2 + σ, where Mn is a complete Riemannian n-manifold with the metric σ, Ω has piecewise smooth boundary, and ℝ denotes the Euclidean 1-space. We prove an interesting stability result for translating spacelike graphs in Mn × ℝ under a conformal transformation.
期刊介绍：
Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981.
The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.
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