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The Dual Blaschke Addition

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Abstract

It is remarkable that there is a duality in geometric tomography between results on projections of convex bodies and results on sections of star (rather than convex) bodies. The radial Blaschke addition, which is the dual version of Blaschke addition, as an operation between central symmetric star bodies is introduced in this paper. The relationship between it and the classical radial addition, many properties of radial Blaschke addition and related inequalities are established.

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Acknowledgements

The authors are very grateful to the referee who read the manuscript carefully and provided a lot of valuable suggestions and comments.

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Authors and Affiliations

  1. Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, Henan, People’s Republic of China

    Lujun Guo & Huahua Jia

Authors
  1. Lujun Guo
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  2. Huahua Jia
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Correspondence to Lujun Guo.

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Supported in part by the National Natural Science Foundation of China (Grant No. 11801151) and Technology Key Project of the Education Department of Henan Province (19A110022).

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Guo, L., Jia, H. The Dual Blaschke Addition. J Geom Anal 30, 3026–3034 (2020). https://doi.org/10.1007/s12220-019-00190-7

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  • DOI: https://doi.org/10.1007/s12220-019-00190-7

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