Asset Details
Do you wish to reserve the book?
On the polar of Schneider's difference body
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
On the polar of Schneider's difference body
Do you wish to request the book?
On the polar of Schneider's difference body
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Paper
On the polar of Schneider's difference body
2025
Overview
In 1970, Schneider introduced the \\(m\\)th-order extension of the difference body \\(DK\\) of a convex body \\(K\\subset\\mathbb R^n\\), the convex body \\(D^m(K)\\) in \\(\\mathbb R^{nm}\\). He conjectured that its volume is minimized for ellipsoids when the volume of \\(K\\) is fixed. In this work, we solve a dual version of this problem: we show that the volume of the polar body of \\(D^m(K)\\) is maximized precisely by ellipsoids. For \\(m=1\\) this recovers the symmetric case of the celebrated Blaschke-Santaló inequality. We also show that Schneider's conjecture cannot be tackled using standard symmetrization techniques, contrary to this new inequality. As an application for our results, we prove Schneider's conjecture asymptotically á la Bourgain-Milman. We also consider a functional version.
Publisher
Cornell University Library, arXiv.org
Subject
We currently cannot retrieve any items related to this title. Kindly check back at a later time.