{"title":"Lipschitz Homeomorphism 的变形","authors":"Mohammad Alattar","doi":"arxiv-2409.06170","DOIUrl":null,"url":null,"abstract":"We obtain the Lipschitz analogues of the results Perelman used from\nSiebenmann's deformation of homeomorphism theory in his proof of the stability\ntheorem. Consequently, we obtain the Lipschitz analogue of Perelman's gluing\ntheorem. Moreover, we obtain the analogous deformation theory but with tracking\nof the Lipschitz constants.","PeriodicalId":501444,"journal":{"name":"arXiv - MATH - Metric Geometry","volume":"28 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Deformations of Lipschitz Homeomorphisms\",\"authors\":\"Mohammad Alattar\",\"doi\":\"arxiv-2409.06170\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We obtain the Lipschitz analogues of the results Perelman used from\\nSiebenmann's deformation of homeomorphism theory in his proof of the stability\\ntheorem. Consequently, we obtain the Lipschitz analogue of Perelman's gluing\\ntheorem. Moreover, we obtain the analogous deformation theory but with tracking\\nof the Lipschitz constants.\",\"PeriodicalId\":501444,\"journal\":{\"name\":\"arXiv - MATH - Metric Geometry\",\"volume\":\"28 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 - Metric Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.06170\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Metric Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06170","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We obtain the Lipschitz analogues of the results Perelman used from
Siebenmann's deformation of homeomorphism theory in his proof of the stability
theorem. Consequently, we obtain the Lipschitz analogue of Perelman's gluing
theorem. Moreover, we obtain the analogous deformation theory but with tracking
of the Lipschitz constants.
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