Pure and Applied Mathematics Quarterly

Volume 19 (2023)

Number 2

Some inequalities for the dual $p$-quermassintegrals

Pages: 681 – 696

DOI: https://dx.doi.org/10.4310/PAMQ.2023.v19.n2.a9

Authors

Weidong Wang (Three Gorges Mathematical Research Center & College of Science, China Three Gorges University, Yichang, China)

Yanping Zhou (Three Gorges Mathematical Research Center & College of Science, China Three Gorges University, Yichang, China)

Abstract

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.

Keywords

dual $p$-quermassintegral, dual $L_q$ Brunn–Minkowski inequality, dual $\log$-Brunn–Minkowsk, Blaschke–Santaló inequality

2010 Mathematics Subject Classification

52A20, 52A40

Received 1 May 2022

Accepted 11 February 2023

Published 7 April 2023