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Mixed complex brightness integrals

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Abstract

The notion of the mixed brightness was first introduced by Lutwak. Recently, Abardia and Bernig presented complex projection bodies. Based on this notion, we define the mixed complex brightness integrals and establish related Aleksandrov–Fenchel inequality, cyclic inequality and monotonicity inequality, respectively.

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Acknowledgements

The authors want to express earnest thankfulness for the referees who provided extremely precious and helpful comments and suggestions.

Author information

Correspondence to Weidong Wang.

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Chao Li: Research is supported in part by the Innovation Foundation of Graduate Student of China Three Gorges University (No.2019SSPY146).

Weidong Wang: Research is supported in part by the Natural Science Foundation of China (No.11371224).

Youjiang Lin: Research is supported in part by the funds of the Basic and Advanced Research Project of CQ CSTC (No.cstc2015jcyjA00009) and Scientific and Technological Research Program of Chongqing Municipal Education Commission (No.KJ1500628).

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Cite this article

Li, C., Wang, W. & Lin, Y. Mixed complex brightness integrals. Positivity 24, 55–67 (2020). https://doi.org/10.1007/s11117-019-00665-5

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Keywords

  • Complex projection body
  • Mixed complex brightness integral
  • Aleksandrov–Fenchel inequality
  • Cyclic inequality
  • Monotonicity inequality

Mathematics Subject Classification

  • 52A20
  • 52A40