Curvature functionals on convex bodies

Kateryna Tatarko, Elisabeth M. Werner

Type: Article

Publication Date: 2022-12-09

Citations: 0

DOI: https://doi.org/10.4153/s0008439522000716

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Abstract

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 Rényi divergence.

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Canadian Mathematical Bulletin - View - PDF
arXiv (Cornell University) - View - PDF

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