A Remark on discrete Brunn-Minkowski type inequalities via transportation of measure

通过最优质量传输的Brunn-Minkowski不等式的精确稳定性

Sharp stability of the Brunn-Minkowski inequality via optimal mass transportation

本文针对Brunn-Minkowski不等式的精确稳定性问题，结合已证明的线性稳定性结果与新颖的最优质量传输方法，给出了关于集合到公共凸包距离的二次稳定性结果的替代证明。

通过熵的凸性研究新的Brunn-Minkowski和函数不等式

New Brunn--Minkowski and functional inequalities via convexity of entropy

本文研究了测度的凹性与相对熵的凸性之间的联系，证明了新的中心星形体的Brunn-Minkowski不等式，并通过Gaussian相对熵的凸性得到新的函数不等式。

关于与奥本-乌尔本克算子相关的布伦-闵克owski型不等式的评论

Remarks on Brunn-Minkowski-type inequalities related to the Ornstein-Uhlenbeck operator

研究与奥本-乌尔本克算子相关的扭转刚度和第一特征值的布伦-闵克owski型不等式，证明扭转刚度在一般有界凸集上不具有凹凸性，且在对称集上证明扭转刚度的1/(n+2)次方既非凸亦非凹，同时证明扭转刚度的1/3次方在欧几里得球上关于闵克owski加法是凸的。

On the stability of Brunn-Minkowski type inequalities

Log-Brunn-Minkowski inequality was conjectured by Boröczky, Lutwak, Yang and Zhang \cite{BLYZ}, and it states that a certain strengthening of the classical Brunn-Minkowski inequality is admissible in the case of symmetric convex sets. It was recently shown by Nayar, Zvavitch, the second and the third authors \cite{LMNZ}, that Log-Brunn-Minkowski inequality implies a certain dimensional Brunn-Minkowski inequality for log-concave measures, which in the case of Gaussian measure was conjectured by Gardner and Zvavitch \cite{GZ}. In this note, we obtain stability results for both Log-Brunn-Minkowsk…

关于运输费用及其不等式的几点注记

Some remarks on transportation cost and related inequalities

讨论了凸体上一致测度的运输费用不等式，以及它与其它几何不等式和泛函不等式的联系。特别地，我们证明了运输不等式如何应用于切片问题，并给出了一个新的log-Sobolev型不等式。

关于一类泛函的 $L_p$ Brunn-Minkowski 型不等式

On $L_p$ Brunn-Minkowski type inequalities for a general class of functionals

本文证明了标准高斯测度和经典 Wills 泛函的 $L_p$ Brunn-Minkowski 型不等式及其等号条件，并基于更一般的泛函方法推广至具有径向递减密度的绝对连续测度。