{"title":"Uniform Metric Graphs","authors":"David A. Herron","doi":"10.1007/s12220-024-01735-1","DOIUrl":null,"url":null,"abstract":"<p>We prove that every complete metric space “is” the boundary of a uniform length space whose quasihyperbolization is a geodesic visual Gromov hyperbolic space. There is a natural quasimöbius identification of the original space’s conformal gauge with the canonical gauge on the Gromov boundary. All parameters are absolute constants.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":"30 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Geometric Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s12220-024-01735-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We prove that every complete metric space “is” the boundary of a uniform length space whose quasihyperbolization is a geodesic visual Gromov hyperbolic space. There is a natural quasimöbius identification of the original space’s conformal gauge with the canonical gauge on the Gromov boundary. All parameters are absolute constants.
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