Lp-Blaschke valuations

Jin Li Shanghai University Shufeng Yuan Shanghai University Gangsong Leng Shanghai University

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
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  title={Lp-Blaschke valuations},
  author={Jin Li, Shufeng Yuan, and Gangsong Leng},
  booktitle={Trans. Amer. Math. Soc.},
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.
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