{"title":"Blaschke度量的极限","authors":"Charles Ouyang, Andrea Tamburelli","doi":"10.1215/00127094-2021-0027","DOIUrl":null,"url":null,"abstract":"We find a compactification of the $\\mathrm{SL}(3,\\mathbb{R})$-Hitchin component by studying the degeneration of the Blaschke metrics on the associated equivariant affine spheres. In the process, we establish the closure in the space of projectivized geodesic currents of the space of flat metrics induced by holomorphic cubic differentials on a Riemann surface.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"14","resultStr":"{\"title\":\"Limits of Blaschke metrics\",\"authors\":\"Charles Ouyang, Andrea Tamburelli\",\"doi\":\"10.1215/00127094-2021-0027\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We find a compactification of the $\\\\mathrm{SL}(3,\\\\mathbb{R})$-Hitchin component by studying the degeneration of the Blaschke metrics on the associated equivariant affine spheres. In the process, we establish the closure in the space of projectivized geodesic currents of the space of flat metrics induced by holomorphic cubic differentials on a Riemann surface.\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2019-11-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1215/00127094-2021-0027\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1215/00127094-2021-0027","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
We find a compactification of the $\mathrm{SL}(3,\mathbb{R})$-Hitchin component by studying the degeneration of the Blaschke metrics on the associated equivariant affine spheres. In the process, we establish the closure in the space of projectivized geodesic currents of the space of flat metrics induced by holomorphic cubic differentials on a Riemann surface.
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