$L_p$-Steiner quermassintegrals
Differential Geometry
2023-07-14 v2
Abstract
Inspired by an Steiner formula for the affine surface area proved by Tatarko and Werner, we define, in analogy to the classical Steiner formula, -Steiner quermassintegrals. Special cases include the classical mixed volumes, the dual mixed volumes, the affine surface areas and the mixed affine surface areas. We investigate the properties of the -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.
Cite
@article{arxiv.2110.08659,
title = {$L_p$-Steiner quermassintegrals},
author = {Kateryna Tatarko and Elisabeth M. Werner},
journal= {arXiv preprint arXiv:2110.08659},
year = {2023}
}