C. Sormani, Demetre Kazaras, David Afrifa, Victoria Antonetti, M. Dinowitz, H. Drillick, M. Farahzad, Shanell George, Aleah Lydeatte Hepburn, Leslie Trang Huynh, Emilio Minichiello, Julinda Mujo Pillati, Srivishnupreeth Rendla, A. Yamin
{"title":"Smocked Metric Spaces and Their Tangent Cones","authors":"C. Sormani, Demetre Kazaras, David Afrifa, Victoria Antonetti, M. Dinowitz, H. Drillick, M. Farahzad, Shanell George, Aleah Lydeatte Hepburn, Leslie Trang Huynh, Emilio Minichiello, Julinda Mujo Pillati, Srivishnupreeth Rendla, A. Yamin","doi":"10.35834/2021/3301027","DOIUrl":null,"url":null,"abstract":"We introduce the notion of a smocked metric spaces and explore the balls and geodesics in a collection of different smocked spaces. We find their rescaled Gromov-Hausdorff limits and prove these tangent cones at infinity exist, are unique, and are normed spaces. We close with a variety of open questions suitable for advanced undergraduates, masters students, and doctoral students.","PeriodicalId":42784,"journal":{"name":"Missouri Journal of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2019-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Missouri Journal of Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.35834/2021/3301027","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
We introduce the notion of a smocked metric spaces and explore the balls and geodesics in a collection of different smocked spaces. We find their rescaled Gromov-Hausdorff limits and prove these tangent cones at infinity exist, are unique, and are normed spaces. We close with a variety of open questions suitable for advanced undergraduates, masters students, and doctoral students.
期刊介绍：
Missouri Journal of Mathematical Sciences (MJMS) publishes well-motivated original research articles as well as expository and survey articles of exceptional quality in mathematical sciences. A section of the MJMS is also devoted to interesting mathematical problems and solutions.
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