Geodesic
Orlicz mixed projection body
Filomat, Tome 37 (2023) no. 18, p. 5895

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DOI

In the paper, our main aim is to generalize the mixed projection body Π(K1, . . . ,Kn−1) of (n − 1) convex bodies K1, . . . ,Kn−1 to the Orlicz space. Under the framework of Orlicz-Brunn-Minkowski theory, we introduce a new affine geometric operation call it Orlicz mixed projection body Πφ(K1, . . . ,Kn) of n convex bodies K1, . . . ,Kn. The new affine geometric quantity in special case yields the classical mixed projection body Π(K1, . . . ,Kn−1) and Orlicz projection body ΠφK of convex body K, respectively. The related concept of Lp-mixed projection body of n convex bodies Πp(K1, . . . ,Kn) is also derived. An Orlicz Alesandrov- Fenchel inequality for the Orlicz mixed projection body is established, which in special case yields a new Lp-projection Alesandrov-Fenchel inequality. As an application, we establish a polar Orlicz Alesandrov- Fenchel inequality for the polar of Orlicz mixed projection body.
DOI : 10.2298/FIL2318895Z
Classification : 46E30, 52A30
Keywords: mixed volume, projection body, mixed projection body, Lp-projection body, Orlicz projection body, Orlicz mixed projection body, Jensen’s inequality, Alesandrov-Fenchel inequality for mixed projection bodies 
Chang-Jian Zhao. Orlicz mixed projection body. Filomat, Tome 37 (2023) no. 18, p. 5895 . doi: 10.2298/FIL2318895Z
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     author = {Chang-Jian Zhao},
     title = {Orlicz mixed projection body},
     journal = {Filomat},
     pages = {5895 },
     year = {2023},
     volume = {37},
     number = {18},
     doi = {10.2298/FIL2318895Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2318895Z/}
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