{"title":"关于 $$p$$ - 质点积分的一些不等式","authors":"Weidong Wang, Yanping Zhou","doi":"10.1134/S0016266323020028","DOIUrl":null,"url":null,"abstract":"<p> In this paper, we generalize the notions of quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals to <span>\\(p\\)</span>-quermassintegrals so that the cases <span>\\(p=1, -1, -n\\)</span> of <span>\\(p\\)</span>-quermassintegrals are quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals, respectively. Further, we obtain some inequalities associated with <span>\\(p\\)</span>-quermassintegrals, including <span>\\(L_q\\)</span> Brunn–Minkowski-type inequalities, a monotonic inequality, and a Bourgain–Milman-type inequality. </p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some Inequalities for \\\\(p\\\\)-Quermassintegrals\",\"authors\":\"Weidong Wang, Yanping Zhou\",\"doi\":\"10.1134/S0016266323020028\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> In this paper, we generalize the notions of quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals to <span>\\\\(p\\\\)</span>-quermassintegrals so that the cases <span>\\\\(p=1, -1, -n\\\\)</span> of <span>\\\\(p\\\\)</span>-quermassintegrals are quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals, respectively. Further, we obtain some inequalities associated with <span>\\\\(p\\\\)</span>-quermassintegrals, including <span>\\\\(L_q\\\\)</span> Brunn–Minkowski-type inequalities, a monotonic inequality, and a Bourgain–Milman-type inequality. </p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-12-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S0016266323020028\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S0016266323020028","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, we generalize the notions of quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals to \(p\)-quermassintegrals so that the cases \(p=1, -1, -n\) of \(p\)-quermassintegrals are quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals, respectively. Further, we obtain some inequalities associated with \(p\)-quermassintegrals, including \(L_q\) Brunn–Minkowski-type inequalities, a monotonic inequality, and a Bourgain–Milman-type inequality.
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