Some Inequalities for -Quermassintegrals.

In this paper, we generalize the notions of quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals to -quermassintegrals so that the cases of -quermassintegrals are quermassintegrals, harmonic quermassintegrals, and affine quermassintegrals, respectively. Further, we obtain some inequalities associated with -quermassintegrals, including Brunn–Minkowski-type inequalities, a monotonic inequality, and a Bourgain–Milman-type inequality. [ABSTRACT FROM AUTHOR]