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 $C_{+}^2$ in $\text{rnnn}$ by using the concavity of related Brunn-Minkowski inequality.