Geodesic
Inequalities for Orlicz Mixed Quermassintegrals
Journal of convex analysis, Tome 26 (2019) no. 1, pp. 129-151
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Our main aim is to generalize the mixed quermassintegrals Wi(K, L) of convex bodies to the Orlicz space. Under the framework of Orlicz-Brunn-Minkowski theory, we introduce a new affine geometric quantity Wϕ,i(M, K, L) by calculating the first Orlicz variation of the mixed quermassintegrals, and call it the Orlicz mixed quermassintegrals of the convex bodies M, K and L. Fundamental notions and properties of mixed quermassintegrals, and the Minkoswki and Brunn-Minkowski inequalities for mixed quermassintegrals are derived in the Orlicz setting. Related concepts and inequalities of a new type of Lp-mixed quermassintegrals Wp,i(M, K, L) are also derived. One of these has connections with the conjectured log-Brunn-Minkowski inequality and we prove a new general log Minkowski type inequality. Finally, we introduce the concept of mixed projection quermassintegrals and prove an Orlicz-Minkowski type inequality for the mixed projection quermassintegrals.
Classification : 52A20, 52A39, 46E30
Mots-clés : L-p-addition, Orlicz addition, mixed quermassintegrals, p-mixed quermassintegrals, Orlicz mixed quermassintegrals, Orlicz projection quermassintegrals 
@article{JCA_2019_26_1_JCA_2019_26_1_a8,
     author = {C.-J. Zhao},
     title = {Inequalities for {Orlicz} {Mixed} {Quermassintegrals}},
     journal = {Journal of convex analysis},
     pages = {129--151},
     year = {2019},
     volume = {26},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2019_26_1_JCA_2019_26_1_a8/}
}
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C.-J. Zhao. Inequalities for Orlicz Mixed Quermassintegrals. Journal of convex analysis, Tome 26 (2019) no. 1, pp. 129-151. http://geodesic.mathdoc.fr/item/JCA_2019_26_1_JCA_2019_26_1_a8/