论文标题
Brunn-Minkowski的不平等现象，$θ$ - 卷卷的身体通过Ball的尸体
Brunn-Minkowski inequality for $θ$-convolution bodies via Ball's bodies
论文作者
论文摘要
我们考虑找到最佳函数$φ_n的问题：[0,1] \ to \ mathbb {r} $，使得对于任何一对凸面$ k，in \ in \ mathbb {r} n $ | k+_θl|^\ frac {1} {n} \ geq或geq或我们证明，在其超级套件中，在$α$ concave功能的鲍尔家族中急剧包括在$ \ left范围内提供最佳功能（\ frac {3} {4} {4} \ right）^n \leqθ\ leq1 $。
We consider the problem of finding the best function $φ_n:[0,1]\to\mathbb{R}$ such that for any pair of convex bodies $K,L\in\mathbb{R}^n$ the following Brunn-Minkowski type inequality holds $$ |K+_θL|^\frac{1}{n}\geqφ_n(θ)(|K|^\frac{1}{n}+|L|^\frac{1}{n}), $$ where $K+_θL$ is the $θ$-convolution body of $K$ and $L$. We prove a sharp inclusion of the family of Ball's bodies of an $α$-concave function in its super-level sets in order to provide the best possible function in the range $\left(\frac{3}{4}\right)^n\leqθ\leq1$, characterizing the equality cases.
