The functional inequality for the mixed quermassintegral

Abstract

Abstract In this paper, the functional Quermassintegrals of a log-concave function in R n $\mathbb{R}^{n}$ are discussed. The functional inequality for the ith mixed Quermassintegral is established. Moreover, as a special case, a weaker log-Quermassintegral inequality in R n $\mathbb{R}^{n}$ is obtained.

Keywords

• Log-concave function
• Quermassintegral
• Mixed Quermassintegral inequality
• Minkowski inequality