# MathSciDoc: An Archive for Mathematician ∫

#### Convex and Discrete Geometry mathscidoc:1703.40032

Trans. Amer. Math. Soc., 367, (5), 3161-3187, 2015
In this article, a classification of continuous, linearly intertwining, symmetric \$L_p\$-Blaschke (\$p>1\$) valuations is established as an extension of Haberl's work on Blaschke valuations. More precisely, we show that for dimensions \$n \geq 3\$, the only continuous, linearly intertwining, normalized symmetric \$L_p\$-Blaschke valuation is the normalized \$L_p\$-curvature image operator, while for dimension \$n = 2 \$, a rotated normalized \$L_p\$-curvature image operator is an only additional one. One of the advantages of our approach is that we deal with normalized symmetric \$L_p\$-Blaschke valuations, which makes it possible to handle the case \$p=n\$. The cases where \$p \neq =n\$ are also discussed by studying the relations between symmetric \$L_p\$-Blaschke valuations and normalized ones.
normalized Lp-Blaschke valuation, normalized Lp-curvature image, Lp-Blaschke valuation, Lp-curvature image
```@inproceedings{jin2015lp-blaschke,
title={Lp-Blaschke valuations},
author={Jin Li, Shufeng Yuan, and Gangsong Leng},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170310015948661107648},
booktitle={Trans. Amer. Math. Soc.},
volume={367},
number={5},
pages={3161-3187},
year={2015},
}
```
Jin Li, Shufeng Yuan, and Gangsong Leng. Lp-Blaschke valuations. 2015. Vol. 367. In Trans. Amer. Math. Soc.. pp.3161-3187. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170310015948661107648.