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The Dual Blaschke Addition

  • Lujun GuoEmail author
  • Huahua Jia
Article
  • 41 Downloads

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.

Keywords

Star body Blaschke addition Radial addition k-Intersection body Dual Brunn–Minkowski inequality 

Mathematical Subject Classification

52A20 52A40 39B22 

Notes

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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Copyright information

© Mathematica Josephina, Inc. 2019

Authors and Affiliations

  1. 1.Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, College of Mathematics and Information ScienceHenan Normal UniversityXinxiangPeople’s Republic of China

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