In this paper, the functional Quermassintegrals of a log-concave function in $\mathbb{R}^{n}$ are discussed. The functional inequality for the ith mixed Quermassintegral is established. Moreover, as a special case, a weaker log-Quermassintegral inequality in $\mathbb{R}^{n}$ is obtained.

中文翻译：

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混合量子积分的泛函不等式

本文讨论了$ \ mathbb {R} ^ {n} $中对数凹函数的函数Quermass积分。建立了第i个混合Quermassintegral的泛函不等式。此外，作为特殊情况，获得了$ \ mathbb {R} ^ {n} $中的弱对数Quermassintegral不等式。