{"title":"凸体的截面和汉纳多面体","authors":"Xinbao Lu, Jiangyan Tao, Ge Xiong","doi":"10.1007/s00208-024-02930-9","DOIUrl":null,"url":null,"abstract":"<p>Bounds for the volume of sections of convex bodies which are in the <span>\\(L_p\\)</span> John ellipsoid positions are established. Specifically, when the convex bodies are in the LYZ ellipsoid position, we construct a set of Hanner polytopes attaining the sharp bounds.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"21 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sections of convex bodies and Hanner polytopes\",\"authors\":\"Xinbao Lu, Jiangyan Tao, Ge Xiong\",\"doi\":\"10.1007/s00208-024-02930-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Bounds for the volume of sections of convex bodies which are in the <span>\\\\(L_p\\\\)</span> John ellipsoid positions are established. Specifically, when the convex bodies are in the LYZ ellipsoid position, we construct a set of Hanner polytopes attaining the sharp bounds.</p>\",\"PeriodicalId\":18304,\"journal\":{\"name\":\"Mathematische Annalen\",\"volume\":\"21 1\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-07-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematische Annalen\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00208-024-02930-9\",\"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":"Mathematische Annalen","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00208-024-02930-9","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Bounds for the volume of sections of convex bodies which are in the \(L_p\) John ellipsoid positions are established. Specifically, when the convex bodies are in the LYZ ellipsoid position, we construct a set of Hanner polytopes attaining the sharp bounds.
期刊介绍：
Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin.
The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin.
Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.
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