凸体的λ Entropy的Brunn-Minkowski不等式
The Brunn-Minkowski Inequalities of λ Entropy of Convex Body
摘要: Borel测度λ绝对连续的假设下，证明了高斯像问题的解存在唯一性。在本文中，我们建立了凸体的λ entropy的Brunn-Minkowski不等式。作为推论，我们给出高斯像问题唯一性的另一证明。注意到，即使测度λ不是绝对连续的，我们所得到的关于λ entropy的Brunn-Minkowski不等式依旧成立。
Abstract: In the paper Gauss Image Problem, Böröczky-Lutwak-Yang-Zhang-Zhao proposed the Gaussian image problem, and under the assumption that the Borel measure λ is absolutely continuous, they proved the existence and uniqueness of the solution of the Gaussian image problem. In this paper, we establish the Brunn-Minkowski type inequality of the λ entropy of convex body. As a corollary, we give another proof of the uniqueness of the Gaussian image problem. Note that even if the measure λ is not absolutely continuous, the Brunn-Minkowski inequality of the λ entropy still holds.
文章引用：张振坤. 凸体的λ Entropy的Brunn-Minkowski不等式[J]. 理论数学, 2021, 11(7): 1361-1368. https://doi.org/10.12677/PM.2021.117153

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