Geodesic
Curvature functionals on convex bodies
Canadian mathematical bulletin, Tome 66 (2023) no. 3, pp. 761-779

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DOI

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.
DOI : 10.4153/S0008439522000716
Mots-clés : Steiner formula, curvature measures, Lp Brunn–Minkowski theory 
Tatarko, Kateryna; Werner, Elisabeth M. Curvature functionals on convex bodies. Canadian mathematical bulletin, Tome 66 (2023) no. 3, pp. 761-779. doi: 10.4153/S0008439522000716
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     title = {Curvature functionals on convex bodies},
     journal = {Canadian mathematical bulletin},
     pages = {761--779},
     year = {2023},
     volume = {66},
     number = {3},
     doi = {10.4153/S0008439522000716},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000716/}
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