{"title":"Gromov-Lawson隧道估算","authors":"J. Dodziuk","doi":"10.1017/9781108615259.004","DOIUrl":null,"url":null,"abstract":"In an appendix to an earlier paper (cf. arXiv:1703.00984) we showed we showed how to construct tunnels of positive scalar curvature and of arbitrarily small length and volume connecting points in a \\emph{three dimensional} manifold of \\emph{constant sectional curvature}. Here we generalize the construction to arbitrary dimensions and require only positivity of the scalar curvature. This version contains an added section on existence of arbitrarily narrow tunnels of prescribed length.","PeriodicalId":393578,"journal":{"name":"Analysis and Geometry on Graphs and Manifolds","volume":"145 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Gromov–Lawson Tunnels with Estimates\",\"authors\":\"J. Dodziuk\",\"doi\":\"10.1017/9781108615259.004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In an appendix to an earlier paper (cf. arXiv:1703.00984) we showed we showed how to construct tunnels of positive scalar curvature and of arbitrarily small length and volume connecting points in a \\\\emph{three dimensional} manifold of \\\\emph{constant sectional curvature}. Here we generalize the construction to arbitrary dimensions and require only positivity of the scalar curvature. This version contains an added section on existence of arbitrarily narrow tunnels of prescribed length.\",\"PeriodicalId\":393578,\"journal\":{\"name\":\"Analysis and Geometry on Graphs and Manifolds\",\"volume\":\"145 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-02-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis and Geometry on Graphs and Manifolds\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/9781108615259.004\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Geometry on Graphs and Manifolds","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/9781108615259.004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In an appendix to an earlier paper (cf. arXiv:1703.00984) we showed we showed how to construct tunnels of positive scalar curvature and of arbitrarily small length and volume connecting points in a \emph{three dimensional} manifold of \emph{constant sectional curvature}. Here we generalize the construction to arbitrary dimensions and require only positivity of the scalar curvature. This version contains an added section on existence of arbitrarily narrow tunnels of prescribed length.
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