Pure and Applied Mathematics Quarterly
Volume 19 (2023)
Some inequalities for the dual $p$-quermassintegrals
Pages: 681 – 696
Based on the definitions of dual quermassintegrals, dual affine quermassintegrals and dual harmonic quermassintegrals, we generalize them to the dual $p$-quermassintegrals, such that the cases $p = 1$ , $n$ and $-1$ just are the dual quermassintegrals, dual affine quermassintegrals and dual harmonic quermassintegrals, respectively. Further, we orderly establish the dual $L_q$ Brunn–Minkowski type inequality, dual $\log$-Brunn–Minkowski type inequality and Blaschke–Santaló type inequality for the dual $p$-quermassintegrals.
dual $p$-quermassintegral, dual $L_q$ Brunn–Minkowski inequality, dual $\log$-Brunn–Minkowsk, Blaschke–Santaló inequality
2010 Mathematics Subject Classification
The authors’ research was supported in part by the Natural Science Foundations of China (Grant No.11371224, 11901346).
Received 1 May 2022
Accepted 11 February 2023
Published 7 April 2023