Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Xi Dongmeng"'
Publikováno v:
Advanced Nonlinear Studies, Vol 23, Iss 1, Pp 907-945 (2023)
Chord measures are newly discovered translation-invariant geometric measures of convex bodies in Rn{{\mathbb{R}}}^{n}, in addition to Aleksandrov-Fenchel-Jessen’s area measures. They are constructed from chord integrals of convex bodies and random
Externí odkaz:
https://doaj.org/article/0fc176d040524ede90edd5979b7dc829
Autor:
Langharst, Dylan, Xi, Dongmeng
In 1970, Schneider introduced the higher-order difference body and the associated Rogers-Shephard inequality. Recently, Haddad, Langharst, Putterman, Roysdon and Ye expanded the concept to a burgeoning higher-order Brunn-Minkowski theory. In 1991, Zh
Externí odkaz:
http://arxiv.org/abs/2312.09500
Autor:
Xi, Dongmeng
Firstly, we propose our conjectured Reverse-log-Brunn-Minkowski inequality (RLBM). Secondly, we show that the (RLBM) conjecture is equivalent to the log-Brunn-Minkowski (LBM) conjecture proposed by B\"or\"oczky-Lutwak-Yang-Zhang. We name this as ``re
Externí odkaz:
http://arxiv.org/abs/2307.04266
Chord measures and $L_p$ chord measures were recently introduced by Lutwak-Xi-Yang-Zhang by establishing a variational formula regarding a family of fundamental integral geometric invariants called chord integrals. Prescribing the $L_p$ chord measure
Externí odkaz:
http://arxiv.org/abs/2301.07603
We introduce dual curvature measures for log-concave functions, which in the case of characteristic functions recover the dual curvature measures for convex bodies introduced by Huang-Lutwak-Yang-Zhang in 2016. Variational formulas are shown. The ass
Externí odkaz:
http://arxiv.org/abs/2210.02359
This paper is dedicated to study the sine version of polar bodies and establish the $L_p$-sine Blaschke-Santal\'{o} inequality for the $L_p$-sine centroid body. The $L_p$-sine centroid body $\Lambda_p K$ for a star body $K\subset\mathbb{R}^n$ is a co
Externí odkaz:
http://arxiv.org/abs/2206.00185
The works of Bennett, Carbery, Christ, Tao and of Valdimarsson have clarified when equality holds in the Brascamp-Lieb inequality. Here we characterize the case of equality in the Geometric case of Barthe's reverse Brascamp-Lieb inequality.
Externí odkaz:
http://arxiv.org/abs/2203.01428
The Minkowski problem in Gaussian probability space is studied in this paper. In addition to providing an existence result on a Gaussian-volume-normalized version of this problem, the main goal of the current work is to provide uniqueness and existen
Externí odkaz:
http://arxiv.org/abs/2010.00395
Autor:
Lin, Youjiang, Xi, Dongmeng
The conjecture about the Orlicz P\'olya-Szeg\"o principle posed in [43] is proved. The cases of equality are characterized in the affine Orlicz P\'olya-Szeg\"o principle with respect to Steiner symmetrization and Schwarz spherical symmetrization.
Externí odkaz:
http://arxiv.org/abs/2008.07026
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