اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA Prekopa-Leindler type inequality of the $L_p$ Brunn-Minkowski inequality
113
0
0.0
(
0
)
تأليف
Yuchi Wu
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper, we prove a Prekopa-Leindler type inequality of the $L_p$ Brunn-Minkowski inequality. It extends an inequality proved by Das Gupta [8] and Klartag [16], and thus recovers the Prekopa-Leindler inequality. In addition, we prove a functional $L_p$ Minkowski inequality.
قيم البحث
اقرأ أيضاً
Henstock and Macbeath asked in 1953 whether the Brunn-Minkowski inequality can be generalized to nonabelian locally compact groups; questions in the same line were also asked by Hrushovski, McCrudden, and Tao. We obtain here such an inequality and pr
ove that it is sharp for helix-free locally compact groups, which includes real linear algebraic groups, Nash groups, semisimple Lie groups with finite center, solvable Lie groups, etc. The proof follows an induction on dimension strategy; new ingredients include an understanding of the role played by maximal compact subgroups of Lie groups, a necessary modified form of the inequality which is also applicable to nonunimodular locally compact groups, and a proportionated averaging trick.
We give a short, self-contained proof of two key results from a paper of four of the authors. The first is a kind of weighted discrete Prekopa-Leindler inequality. This is then applied to show that if $A, B subseteq mathbb{Z}^d$ are finite sets and $
U$ is a subset of a quasicube then $|A + B + U| geq |A|^{1/2} |B|^{1/2} |U|$. This result is a key ingredient in forthcoming work of the fifth author and Palvolgyi on the sum-product phenomenon.
We present an alternative, short proof of a recent discrete version of the Brunn-Minkowski inequality due to Lehec and the second named author. Our proof also yields the four functions theorem of Ahlswede and Daykin as well as some new variants.
We prove an analogue of the classical Steiner formula for the $L_p$ affine surface area of a Minkowski outer parallel body for any real parameters $p$. We show that the classical Steiner formula and the Steiner formula of Lutwaks dual Brunn Minkowski
theory are special cases of this new Steiner formula. This new Steiner formula and its localiz
We give an alternative proof for discrete Brunn-Minkowski type inequalities, recently obtained by Halikias, Klartag and the author. This proof also implies somewhat stronger weight
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
