Geodesic
Some inequalities for $p$-quermassintegrals
Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 2, pp. 18-30

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In this paper, we generalize the notions of quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals to $p$-quermassintegrals so that the cases $p=1, -1, -n$ of $p$-quermassintegrals are quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals, respectively. Further, we obtain some inequalities associated with $p$-quermassintegrals, including $L_q$ Brunn–Minkowski-type inequalities, a monotonic inequality, and a Bourgain–Milman-type inequality.
Keywords: quermassintegral, harmonic quermassintegral, affine quermassintegral, $p$-quermassintegral, $L_q$ Brunn–Minkowski inequality, monotonic inequality, Bourgain–Milman inequality. 
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     author = {W. Wang and Ya. Zhou},
     title = {Some inequalities for $p$-quermassintegrals},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
     volume = {57},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2023_57_2_a1/}
}
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W. Wang; Ya. Zhou. Some inequalities for $p$-quermassintegrals. Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 2, pp. 18-30. http://geodesic.mathdoc.fr/item/FAA_2023_57_2_a1/