{"title":"A Bogovskiǐ-type operator for Corvino-Schoen hyperbolic gluing","authors":"Piotr T. Chruściel, Albachiara Cogo, Andrea Nützi","doi":"arxiv-2409.07502","DOIUrl":null,"url":null,"abstract":"We construct a solution operator for the linearized constant scalar curvature\nequation at hyperbolic space in space dimension larger than or equal to two.\nThe solution operator has good support propagation properties and gains two\nderivatives relative to standard norms. It can be used for Corvino-Schoen-type\nhyperbolic gluing, partly extending the recently introduced Mao-Oh-Tao gluing\nmethod to the hyperbolic setting.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"49 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07502","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We construct a solution operator for the linearized constant scalar curvature
equation at hyperbolic space in space dimension larger than or equal to two.
The solution operator has good support propagation properties and gains two
derivatives relative to standard norms. It can be used for Corvino-Schoen-type
hyperbolic gluing, partly extending the recently introduced Mao-Oh-Tao gluing
method to the hyperbolic setting.
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