Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds

Ai-Jun Li Henan Polytechnic University Dongmeng Xi Shanghai University Gaoyong Zhang New York University

Convex and Discrete Geometry mathscidoc:1703.40021

Advances in Mathematics, 304, 494–538, 2017.1
The $L_p$ cosine transform on Grassmann manifolds naturally induces finite dimensional Banach norms whose unit balls are origin-symmetric convex bodies in $\rn$. Reverse isoperimetric type volume inequalities for these bodies are established, which extend results from the sphere to Grassmann manifolds.
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@inproceedings{ai-jun2017volume,
  title={Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds},
  author={Ai-Jun Li, Dongmeng Xi, and Gaoyong Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170304090229963947607},
  booktitle={Advances in Mathematics},
  volume={304},
  pages={494–538},
  year={2017},
}
Ai-Jun Li, Dongmeng Xi, and Gaoyong Zhang. Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds. 2017. Vol. 304. In Advances in Mathematics. pp.494–538. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170304090229963947607.
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