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 Poincaré-type inequalities for torsional rigidity on the boundary of a convex body of class \(C^{2}_{+}\) $C_{+}^2$ in \(\mathbb {R}^n\) ${\mathbb{R}}^n$ by using the concavity of related Brunn-Minkowski inequality.