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arXiv · 1602.05994

Monotonicity and concavity of integral functionals involving area measures of convex bodies

Andrea Colesanti·Daniel Hug·Eugenia Saorín-Gómez
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Abstract

For a broad class of integral functionals defined on the space of $n$-dimensional convex bodies, we establish necessary and sufficient conditions for monotonicity, and necessary conditions for the validity of a Brunn-Minkowski type inequality. In particular, we prove that a Brunn-Minkowski type inequality implies monotonicity, and that a general Brunn-Minkowski type inequality is equivalent to the functional being a mixed volume.

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Andrea Colesanti, Daniel Hug, Eugenia Saorín-Gómez. 2016-02-18. Monotonicity and concavity of integral functionals involving area measures of convex bodies. https://arxiv.org/abs/1602.05994

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