{"title":"加权图上拉普拉斯算子的一般下界","authors":"D. Lenz, P. Stollmann","doi":"10.1017/9781108615259.009","DOIUrl":null,"url":null,"abstract":"We discuss optimal lower bounds for eigenvalues of Laplacians on weighted graphs. These bounds are formulated in terms of the geometry and, more specifically, the inradius of subsets of the graph. In particular, we study the first non-zero eigenvalue in the finite volume case and the first eigenvalue of the Dirichlet Laplacian on subsets that satisfy natural geometric conditions.","PeriodicalId":393578,"journal":{"name":"Analysis and Geometry on Graphs and Manifolds","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Universal Lower Bounds for Laplacians on Weighted Graphs\",\"authors\":\"D. Lenz, P. Stollmann\",\"doi\":\"10.1017/9781108615259.009\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We discuss optimal lower bounds for eigenvalues of Laplacians on weighted graphs. These bounds are formulated in terms of the geometry and, more specifically, the inradius of subsets of the graph. In particular, we study the first non-zero eigenvalue in the finite volume case and the first eigenvalue of the Dirichlet Laplacian on subsets that satisfy natural geometric conditions.\",\"PeriodicalId\":393578,\"journal\":{\"name\":\"Analysis and Geometry on Graphs and Manifolds\",\"volume\":\"7 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-03-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis and Geometry on Graphs and Manifolds\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/9781108615259.009\",\"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/10.1017/9781108615259.009","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Universal Lower Bounds for Laplacians on Weighted Graphs
We discuss optimal lower bounds for eigenvalues of Laplacians on weighted graphs. These bounds are formulated in terms of the geometry and, more specifically, the inradius of subsets of the graph. In particular, we study the first non-zero eigenvalue in the finite volume case and the first eigenvalue of the Dirichlet Laplacian on subsets that satisfy natural geometric conditions.
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