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In this paper, we establish a class of generalized Poincar\'{e}-typeinequalities for torsional rigidity on the boundary of a convex body of class$C^{2}_{+}$ in $\rnnn$ by using the concavity of related Brunn-Minkowskiinequality.

From the Brunn-Minkowski inequality to a class of generalized Poincar\'{e}-type inequalities for torsional rigidity