{"title":"有限子集外曲率为非负的图形、谐函数和端点数","authors":"Bobo Hua, Florentin Münch","doi":"10.1112/jlms.70034","DOIUrl":null,"url":null,"abstract":"<p>We study graphs with nonnegative Bakry–Émery curvature or Ollivier curvature outside a finite subset. For such a graph, via introducing the discrete Gromov–Hausdorff convergence, we prove that the space of bounded harmonic functions is finite dimensional and, as a corollary, the number of nonparabolic ends is finite.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 6","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Graphs with nonnegative curvature outside a finite subset, harmonic functions, and number of ends\",\"authors\":\"Bobo Hua, Florentin Münch\",\"doi\":\"10.1112/jlms.70034\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study graphs with nonnegative Bakry–Émery curvature or Ollivier curvature outside a finite subset. For such a graph, via introducing the discrete Gromov–Hausdorff convergence, we prove that the space of bounded harmonic functions is finite dimensional and, as a corollary, the number of nonparabolic ends is finite.</p>\",\"PeriodicalId\":49989,\"journal\":{\"name\":\"Journal of the London Mathematical Society-Second Series\",\"volume\":\"110 6\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-11-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the London Mathematical Society-Second Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70034\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70034","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Graphs with nonnegative curvature outside a finite subset, harmonic functions, and number of ends
We study graphs with nonnegative Bakry–Émery curvature or Ollivier curvature outside a finite subset. For such a graph, via introducing the discrete Gromov–Hausdorff convergence, we prove that the space of bounded harmonic functions is finite dimensional and, as a corollary, the number of nonparabolic ends is finite.
期刊介绍：
The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.
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