{"title":"多边形的小扰动","authors":"Christian Kipp","doi":"10.1016/j.jfa.2024.110644","DOIUrl":null,"url":null,"abstract":"<div><p>Motivated by first-order conditions for extremal bodies of geometric functionals, we study a functional analytic notion of infinitesimal perturbations of convex bodies and give a full characterization of the set of realizable perturbations if the perturbed body is a polytope. As an application, we derive a necessary condition for polytopal maximizers of the isotropic constant.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"287 12","pages":"Article 110644"},"PeriodicalIF":1.7000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S002212362400332X/pdfft?md5=e462643d71502f41002932b5ab067bea&pid=1-s2.0-S002212362400332X-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Small perturbations of polytopes\",\"authors\":\"Christian Kipp\",\"doi\":\"10.1016/j.jfa.2024.110644\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Motivated by first-order conditions for extremal bodies of geometric functionals, we study a functional analytic notion of infinitesimal perturbations of convex bodies and give a full characterization of the set of realizable perturbations if the perturbed body is a polytope. As an application, we derive a necessary condition for polytopal maximizers of the isotropic constant.</p></div>\",\"PeriodicalId\":15750,\"journal\":{\"name\":\"Journal of Functional Analysis\",\"volume\":\"287 12\",\"pages\":\"Article 110644\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S002212362400332X/pdfft?md5=e462643d71502f41002932b5ab067bea&pid=1-s2.0-S002212362400332X-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Functional Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S002212362400332X\",\"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 Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002212362400332X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Motivated by first-order conditions for extremal bodies of geometric functionals, we study a functional analytic notion of infinitesimal perturbations of convex bodies and give a full characterization of the set of realizable perturbations if the perturbed body is a polytope. As an application, we derive a necessary condition for polytopal maximizers of the isotropic constant.
期刊介绍：
The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published.
Research Areas Include:
• Significant applications of functional analysis, including those to other areas of mathematics
• New developments in functional analysis
• Contributions to important problems in and challenges to functional analysis
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