Estimates of Torsional Rigidity Using Conformal Characteristics.

We consider the Saint Venant functional for the torsional rigidity in simply connected plane domains. We prove new lower and upper estimates of using integrals of the conformal radius defined at any point of the domain and considered as a function. Applications of Davenport's formula for the torsional rigidity are discussed. In addition, we present a short https://doi.org/ of the Saint Venant–Pólya isoperimetric inequality. [ABSTRACT FROM AUTHOR]