Abstract
Inspired by an Lp Steiner formula for the Lp affine surface area proved by Tatarko and Werner, we define, in analogy to the classical Steiner formula, Lp-Steiner quermassintegrals. Special cases include the classical mixed volumes, the dual mixed volumes, the Lp affine surface areas and the mixed Lp affine surface areas. We investigate the properties of the Lp-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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