{"title":"等曲率空间中的等宽凸体与勒洛三角形的极值区","authors":"K. Boroczky, Á. Sagmeister","doi":"10.1556/012.2022.01528","DOIUrl":null,"url":null,"abstract":"Extending Blaschke and Lebesgue’s classical result in the Euclidean plane, it has been recently proved in spherical and the hyperbolic cases, as well, that Reuleaux triangles have the minimal area among convex domains of constant width D. We prove an essentially optimal stability version of this statement in each of the three types of surfaces of constant curvature. In addition, we summarize the fundamental properties of convex bodies of constant width in spaces of constant curvature, and provide a characterization in the hyperbolic case in terms of horospheres.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"108 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Convex Bodies of Constant Width in Spaces of Constant Curvature and the Extremal Area of Reuleaux Triangles\",\"authors\":\"K. Boroczky, Á. Sagmeister\",\"doi\":\"10.1556/012.2022.01528\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Extending Blaschke and Lebesgue’s classical result in the Euclidean plane, it has been recently proved in spherical and the hyperbolic cases, as well, that Reuleaux triangles have the minimal area among convex domains of constant width D. We prove an essentially optimal stability version of this statement in each of the three types of surfaces of constant curvature. In addition, we summarize the fundamental properties of convex bodies of constant width in spaces of constant curvature, and provide a characterization in the hyperbolic case in terms of horospheres.\",\"PeriodicalId\":51187,\"journal\":{\"name\":\"Studia Scientiarum Mathematicarum Hungarica\",\"volume\":\"108 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-03-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Studia Scientiarum Mathematicarum Hungarica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1556/012.2022.01528\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Scientiarum Mathematicarum Hungarica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1556/012.2022.01528","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Convex Bodies of Constant Width in Spaces of Constant Curvature and the Extremal Area of Reuleaux Triangles
Extending Blaschke and Lebesgue’s classical result in the Euclidean plane, it has been recently proved in spherical and the hyperbolic cases, as well, that Reuleaux triangles have the minimal area among convex domains of constant width D. We prove an essentially optimal stability version of this statement in each of the three types of surfaces of constant curvature. In addition, we summarize the fundamental properties of convex bodies of constant width in spaces of constant curvature, and provide a characterization in the hyperbolic case in terms of horospheres.
期刊介绍:
The journal publishes original research papers on various fields of mathematics, e.g., algebra, algebraic geometry, analysis, combinatorics, dynamical systems, geometry, mathematical logic, mathematical statistics, number theory, probability theory, set theory, statistical physics and topology.