{"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}
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.
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.