Iterations of the projection body operator and a remark on Petty's conjectured projection inequality
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- 作者：C. Saroglou <sup>csaroglo@kent.edu" class="auth_mail" title="E-mail the corresponding authorsup> <sup>christos.saroglou@gmail.com" class="auth_mail" title="E-mail the corresponding authorsup> ; A. Zvavitch<sup> ; sup><sup>1sup><sup> ; sup><sup>zvavitch@math.kent.edu" class="auth_mail" title="E-mail the corresponding authorsup>
- 关键词：52A20 ; 53A15 ; 52A39
- 刊名：Journal of Functional Analysis
- 出版年：2017
- 出版时间：15 January 2017
- 年：2017
- 卷：272
- 期：2
- 页码：613-630
- 全文大小：382 K
文摘
We prove that if a convex body has an absolutely continuous surface area measure, whose density is sufficiently close to a constant function, then the sequence rc">rmulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123616302257&_mathId=si1.gif&_user=111111111&_pii=S0022123616302257&_rdoc=1&_issn=00221236&md5=3807b0b3b315896b37164e2ac22f24eb" title="Click to view the MathML source">{Π<sup>msup>K}r hidden"> of convex bodies converges to the ball with respect to the Banach–Mazur distance, as rc">rmulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123616302257&_mathId=si2.gif&_user=111111111&_pii=S0022123616302257&_rdoc=1&_issn=00221236&md5=80a0b208a67afc1857cc66ae99e83090" title="Click to view the MathML source">m→∞r hidden">. Here, Π denotes the projection body operator. Our result allows us to show that the ellipsoid is a local solution to the conjectured inequality of Petty and to improve a related inequality of Lutwak.