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<p>In this paper, we study an optimization problem of Orlicz mixed volume for multiple convex bodies and prove the existence and uniqueness of the solution. According to the existence and uniqueness of the solution, the concept of Orlicz mixed John ellipsoids is introduced. As an application, we establish the volume ratio inequality. In addition, the connection between the isotropy measure and the characterization of Orlicz mixed John ellipsoids is demonstrated.</p>

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Orlicz mixed John ellipsoid

  • 期刊论文

  • 发表日期：

    2025年5月25日

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  • Chao Li

摘要

In this paper, we study an optimization problem of Orlicz mixed volume for multiple convex bodies and prove the existence and uniqueness of the solution. According to the existence and uniqueness of the solution, the concept of Orlicz mixed John ellipsoids is introduced. As an application, we establish the volume ratio inequality. In addition, the connection between the isotropy measure and the characterization of Orlicz mixed John ellipsoids is demonstrated.