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arXiv · 2204.07611

Curvature functionals on convex bodies

Kateryna Tatarko·Elisabeth M. Werner
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Abstract

We investigate the weighted $L_p$ affine surface areas which appear in the recently established $L_p$ Steiner formula of the $L_p$ Brunn Minkowski theory. We show that they are valuations on the set of convex bodies and prove isoperimetric inequalities for them. We show that they are related to $f$ divergences of the cone measures of the convex body and its polar, namely the Kullback-Leibler divergence and the R\'enyi-divergence.

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Kateryna Tatarko, Elisabeth M. Werner. 2022-04-15. Curvature functionals on convex bodies. https://arxiv.org/abs/2204.07611

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