{"title":"关于闭双曲面的极小直径","authors":"Thomas Budzinski, N. Curien, Bram Petri","doi":"10.1215/00127094-2020-0083","DOIUrl":null,"url":null,"abstract":"We prove that the minimal diameter of a hyperbolic compact orientable surface of genus $g$ is asymptotic to $\\log g$ as $g \\to \\infty$. The proof relies on a random construction, which we analyse using lattice point counting theory and the exploration of random trivalent graphs.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2019-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"On the minimal diameter of closed hyperbolic surfaces\",\"authors\":\"Thomas Budzinski, N. Curien, Bram Petri\",\"doi\":\"10.1215/00127094-2020-0083\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the minimal diameter of a hyperbolic compact orientable surface of genus $g$ is asymptotic to $\\\\log g$ as $g \\\\to \\\\infty$. The proof relies on a random construction, which we analyse using lattice point counting theory and the exploration of random trivalent graphs.\",\"PeriodicalId\":11447,\"journal\":{\"name\":\"Duke Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2019-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Duke Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1215/00127094-2020-0083\",\"RegionNum\":1,\"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":"Duke Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1215/00127094-2020-0083","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the minimal diameter of closed hyperbolic surfaces
We prove that the minimal diameter of a hyperbolic compact orientable surface of genus $g$ is asymptotic to $\log g$ as $g \to \infty$. The proof relies on a random construction, which we analyse using lattice point counting theory and the exploration of random trivalent graphs.
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