Orlicz version of mixed moment tensors
DOI:
https://doi.org/10.33044/revuma.2181Abstract
Our main aim is to generalize the moment tensors $\mathbf{\Psi}_{r}(K)$ to the Orlicz space. Under the framework of the Orlicz–Brunn–Minkowski theory, we introduce a new affine geometric quantity $\mathbf{\Psi}_{\psi,r}(K,L)$, and call it Orlicz mixed moment tensors of convex bodies $K$ and $L$. The fundamental notions and properties of the moment tensors as well as related Minkowski and Brunn–Minkowski inequalities are then extended to the Orlicz setting. Diverse inequalities for certain new $L_p$-mixed moment tensors $\mathbf{\Psi}_{p,r}(K,L)$ are also derived. The new Orlicz inequalities in special cases yield the Orlicz–Minkowski and the Orlicz–Brunn–Minkowski inequalities, respectively.
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