Jang方程解的爆破速率控制及其在Penrose不等式上的应用

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Wenhuan Yu
{"title":"Jang方程解的爆破速率控制及其在Penrose不等式上的应用","authors":"Wenhuan Yu","doi":"10.7916/d8-avnq-g588","DOIUrl":null,"url":null,"abstract":"We prove that the blowup term of a blowup solution of Jang's equation on an initial data set (M,g,k) near an arbitrary strictly stable MOTS $ \\Sigma $ is exactly $ -\\frac{1}{\\sqrt{\\lambda}}\\log \\tau $, where $ \\tau $ is the distance from $ \\Sigma $ and $ \\lambda $ is the principal eigenvalue of the MOTS stability operator of $ \\Sigma $. We also prove that the gradient of the solution is of order $ \\tau^{-1} $. Moreover, we apply these results to get a Penrose-like inequality under additional assumptions.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2019-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Blowup rate control for solution of Jang’s equation and its application to Penrose inequality\",\"authors\":\"Wenhuan Yu\",\"doi\":\"10.7916/d8-avnq-g588\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the blowup term of a blowup solution of Jang's equation on an initial data set (M,g,k) near an arbitrary strictly stable MOTS $ \\\\Sigma $ is exactly $ -\\\\frac{1}{\\\\sqrt{\\\\lambda}}\\\\log \\\\tau $, where $ \\\\tau $ is the distance from $ \\\\Sigma $ and $ \\\\lambda $ is the principal eigenvalue of the MOTS stability operator of $ \\\\Sigma $. We also prove that the gradient of the solution is of order $ \\\\tau^{-1} $. Moreover, we apply these results to get a Penrose-like inequality under additional assumptions.\",\"PeriodicalId\":50848,\"journal\":{\"name\":\"Advances in Theoretical and Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2019-06-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Theoretical and Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.7916/d8-avnq-g588\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.7916/d8-avnq-g588","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0

摘要

证明了在任意严格稳定MOTS $ \Sigma $附近的初始数据集(M,g,k)上Jang方程的爆破解的爆破项恰好为$ -\frac{1}{\sqrt{\lambda}}\log \tau $,其中$ \tau $为到$ \Sigma $的距离,$ \lambda $为$ \Sigma $的MOTS稳定性算子的主特征值。我们还证明了解的梯度为$ \tau^{-1} $阶。此外,我们将这些结果应用于在附加假设下的类penrose不等式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Blowup rate control for solution of Jang’s equation and its application to Penrose inequality
We prove that the blowup term of a blowup solution of Jang's equation on an initial data set (M,g,k) near an arbitrary strictly stable MOTS $ \Sigma $ is exactly $ -\frac{1}{\sqrt{\lambda}}\log \tau $, where $ \tau $ is the distance from $ \Sigma $ and $ \lambda $ is the principal eigenvalue of the MOTS stability operator of $ \Sigma $. We also prove that the gradient of the solution is of order $ \tau^{-1} $. Moreover, we apply these results to get a Penrose-like inequality under additional assumptions.
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 Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信