From the Brunn-Minkowski Inequality to a Class of Generalized Poincaré-Type Inequalities for Torsional Rigidity

In this paper, we establish a class of generalized Poincare-type inequalities for torsional rigidity on the boundary of a convex body of class C+2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C<<^>>{2}_{+}$$\end{document} in Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}<<^>>n$$\end{document} by using the concavity of related Brunn-Minkowski inequality.