{"title":"关于 Lp 表面积的斯坦纳不等式","authors":"Zixin Cao , Tuo Wang , Yanhui Wang","doi":"10.1016/j.aim.2024.109997","DOIUrl":null,"url":null,"abstract":"<div><div>The Steiner inequalities for the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> surface area are established for <span><math><mi>p</mi><mo>></mo><mn>1</mn></math></span>. As a consequence, we give a new proof of Lutwak's <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> isoperimetric inequalities for <span><math><mi>p</mi><mo>></mo><mn>1</mn></math></span> together with their equality conditions.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"458 ","pages":"Article 109997"},"PeriodicalIF":1.5000,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Steiner inequality for the Lp surface area\",\"authors\":\"Zixin Cao , Tuo Wang , Yanhui Wang\",\"doi\":\"10.1016/j.aim.2024.109997\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The Steiner inequalities for the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> surface area are established for <span><math><mi>p</mi><mo>></mo><mn>1</mn></math></span>. As a consequence, we give a new proof of Lutwak's <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> isoperimetric inequalities for <span><math><mi>p</mi><mo>></mo><mn>1</mn></math></span> together with their equality conditions.</div></div>\",\"PeriodicalId\":50860,\"journal\":{\"name\":\"Advances in Mathematics\",\"volume\":\"458 \",\"pages\":\"Article 109997\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0001870824005139\",\"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":"Advances in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0001870824005139","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The Steiner inequalities for the surface area are established for . As a consequence, we give a new proof of Lutwak's isoperimetric inequalities for together with their equality conditions.
期刊介绍：
Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.
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