{"title":"广义阿波罗包装的残集维度","authors":"Daniel Lautzenheiser","doi":"10.1007/s10711-024-00899-y","DOIUrl":null,"url":null,"abstract":"<p>We view space-filling circle packings as subsets of the boundary of hyperbolic space subject to symmetry conditions based on a discrete group of isometries. This allows for the application of counting methods which admit rigorous upper and lower bounds on the Hausdorff dimension of the residual set of a generalized Apollonian circle packing. This dimension (which also coincides with a critical exponent) is strictly greater than that of the Apollonian packing.\n</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"11 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The residual set dimension of a generalized apollonian packing\",\"authors\":\"Daniel Lautzenheiser\",\"doi\":\"10.1007/s10711-024-00899-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We view space-filling circle packings as subsets of the boundary of hyperbolic space subject to symmetry conditions based on a discrete group of isometries. This allows for the application of counting methods which admit rigorous upper and lower bounds on the Hausdorff dimension of the residual set of a generalized Apollonian circle packing. This dimension (which also coincides with a critical exponent) is strictly greater than that of the Apollonian packing.\\n</p>\",\"PeriodicalId\":55103,\"journal\":{\"name\":\"Geometriae Dedicata\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-03-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometriae Dedicata\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10711-024-00899-y\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometriae Dedicata","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10711-024-00899-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The residual set dimension of a generalized apollonian packing
We view space-filling circle packings as subsets of the boundary of hyperbolic space subject to symmetry conditions based on a discrete group of isometries. This allows for the application of counting methods which admit rigorous upper and lower bounds on the Hausdorff dimension of the residual set of a generalized Apollonian circle packing. This dimension (which also coincides with a critical exponent) is strictly greater than that of the Apollonian packing.
期刊介绍：
Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems.
Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include:
A fast turn-around time for articles.
Special issues centered on specific topics.
All submitted papers should include some explanation of the context of the main results.
Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.
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