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Orlicz Extensions of Brunn–Minkowski Theory

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Abstract

In the classical Brunn–Minkowski theory, a fruitful principle for obtaining new functionals is to apply familiar functionals, such as the volume \(V_n\), to a Minkowski linear combination \(K+\epsilon L\). This approach can also be used for Orlicz combinations. In this paper, applying the mixed volume functional to Orlicz combination, we introduced the Orlicz mixed volumes and proved the variational formula for the mixed volume with respect to the Orlicz combination. Furthermore, the Orlicz mixed Minkowski inequality and the Orlicz mixed Brunn–Minkowski inequality are established and the equivalence between the inequalities is demonstrated.

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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

    Ruifang Chen & Lujun Guo

Authors
  1. Ruifang Chen
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  2. Lujun Guo
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Corresponding author

Correspondence to Lujun Guo.

Additional information

Ruifang Chen: Supported in part by the National Natural Science Foundation of China (Grant No. U1504101). Lujun Guo: Supported in part by the National Natural Science Foundation of China (Grant No.11526079).

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Chen, R., Guo, L. Orlicz Extensions of Brunn–Minkowski Theory. Results Math 73, 50 (2018). https://doi.org/10.1007/s00025-018-0811-z

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  • DOI: https://doi.org/10.1007/s00025-018-0811-z

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