{"title":"全形射流沿子曲率的最优全形扩展的渐近性","authors":"","doi":"10.1016/j.matpur.2024.06.001","DOIUrl":null,"url":null,"abstract":"<div><p>For a complex submanifold in a complex manifold, we consider the operator which for a given holomorphic jet of a vector bundle along the submanifold associates the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-optimal holomorphic extension of it to the ambient manifold. When the vector bundle is given by big tensor powers of a positive line bundle, we give an asymptotic formula for this extension operator.</p></div>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S002178242400076X/pdfft?md5=403e748e3c30fd29eb21bce9d4dcd45a&pid=1-s2.0-S002178242400076X-main.pdf","citationCount":"0","resultStr":"{\"title\":\"The asymptotics of the optimal holomorphic extensions of holomorphic jets along submanifolds\",\"authors\":\"\",\"doi\":\"10.1016/j.matpur.2024.06.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For a complex submanifold in a complex manifold, we consider the operator which for a given holomorphic jet of a vector bundle along the submanifold associates the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-optimal holomorphic extension of it to the ambient manifold. When the vector bundle is given by big tensor powers of a positive line bundle, we give an asymptotic formula for this extension operator.</p></div>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S002178242400076X/pdfft?md5=403e748e3c30fd29eb21bce9d4dcd45a&pid=1-s2.0-S002178242400076X-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S002178242400076X\",\"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://www.sciencedirect.com/science/article/pii/S002178242400076X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
The asymptotics of the optimal holomorphic extensions of holomorphic jets along submanifolds
For a complex submanifold in a complex manifold, we consider the operator which for a given holomorphic jet of a vector bundle along the submanifold associates the -optimal holomorphic extension of it to the ambient manifold. When the vector bundle is given by big tensor powers of a positive line bundle, we give an asymptotic formula for this extension operator.
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