{"title":"C^{1,1-ε}$ 等距嵌入","authors":"Ángel D. Martínez","doi":"arxiv-2409.00440","DOIUrl":null,"url":null,"abstract":"In this paper we use the convex integration technique enhanced by an extra\niteration originally due to K\\\"all\\'en and revisited by Kr\\\"oner to provide a\nlocal $h$-principle for isometric embeddings in the class $C^{1,1-\\epsilon}$\nfor $n$-dimensional manifolds in codimension $\\frac{1}{2}n(n+1)$.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"$C^{1,1-ε}$ Isometric embeddings\",\"authors\":\"Ángel D. Martínez\",\"doi\":\"arxiv-2409.00440\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we use the convex integration technique enhanced by an extra\\niteration originally due to K\\\\\\\"all\\\\'en and revisited by Kr\\\\\\\"oner to provide a\\nlocal $h$-principle for isometric embeddings in the class $C^{1,1-\\\\epsilon}$\\nfor $n$-dimensional manifolds in codimension $\\\\frac{1}{2}n(n+1)$.\",\"PeriodicalId\":501113,\"journal\":{\"name\":\"arXiv - MATH - Differential Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-31\",\"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-2409.00440\",\"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 - Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.00440","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper we use the convex integration technique enhanced by an extra
iteration originally due to K\"all\'en and revisited by Kr\"oner to provide a
local $h$-principle for isometric embeddings in the class $C^{1,1-\epsilon}$
for $n$-dimensional manifolds in codimension $\frac{1}{2}n(n+1)$.
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