The Busemann intersection inequality states that if K is a compact domain in \({\mathbb {R}}^n\) then

where \(c(n)>0\) is an explicit constant, with equality if and only if K is an ellipsoid centered at the origin. In this paper, we prove a functional version of the Busemann intersection inequality. We also demonstrate an “equivalent” sharp entropy inequality for dual mixed volumes of functions.

中文翻译：

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功能性Busemann相交不等式

Busemann相交不等式指出，如果K是\（{\ mathbb {R}} ^ n \）中的紧域，则

其中\（c（n）> 0 \）是一个显式常数，当且仅当K是一个以原点为中心的椭圆体时，才相等。在本文中，我们证明了Busemann相交不等式的函数形式。我们还证明了函数双重混合体积的“等效”尖锐熵不等式。