论文题目：A unified treatment for Lp Brunn-Minkowski type inequalities

论文作者：Zou Du, Xiong Ge

发表刊物：Communications in Analysis and Geometry

成果介绍：

本文证明了一个准则：若定义在凸体类上的非负泛函是正齐次单调增且凹的，则该泛函是p-凹的。 进一步的，若泛函还是严格增的，则不等式中等号成立当且仅当两个凸体互为膨胀。作为该准则有效性的应用和实证，本文建立了几个新的Lp Brunn-Minkowski 型不等式。这其中包括把著名数学家 C. Borell (Math. Ann. 263 (1983), 179-184.), L. Caffarelli, D. Jerison 和 E. Lieb (Adv. Math. 117 (1996), 193-207.) 建立的电容的 Brunn-Minkowski 型不等式推广到了Lp情形。

此结果受到审稿专家的高度评价。譬如，“... Of the new inequalities obtained I might single out the Lp version of the general capacitary Brunn-Minkowski inequality as a particular nice consequence of this new principle. … I find it remarkable that the main result, Theorem 1.1, has not been published before (as far as I am aware) . … I am sure it will be used and cited very often in the future. ”

所属学科：基础数学，凸几何

论文地址：http://intlpress.com/site/pub/pages/journals/items/cag/_home/_main/