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Summary
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.
