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arXiv · 2110.08659

$L_p$-Steiner quermassintegrals

Kateryna Tatarko·Elisabeth M. Werner
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Abstract

Inspired by an $L_p$ Steiner formula for the $L_p$ affine surface area proved by Tatarko and Werner, we define, in analogy to the classical Steiner formula, $L_p$-Steiner quermassintegrals. Special cases include the classical mixed volumes, the dual mixed volumes, the $L_p$ affine surface areas and the mixed $L_p$ affine surface areas. We investigate the properties of the $L_p$-Steiner quermassintegrals in a special class of convex bodies. In particular, we show that they are rotation and reflection invariant valuations in this class of convex bodies with a certain degree of homogeneity. Such valuations seem new and have not been observed before.

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Kateryna Tatarko, Elisabeth M. Werner. 2021-10-16. $L_p$-Steiner quermassintegrals. https://arxiv.org/abs/2110.08659

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