On the relations between principal eigenvalue and torsional rigidity

The relations between principal eigenvalue of the Laplace operator and torsional rigidity are studied in the class of general domains, convex domains, and domains with a small thickness. This is of help to provide some bounds for the Blasche-Santaló diagram of the two quantities. The results have been obtained in a joint work with Michiel van den Berg (Bristol) and Aldo Pratelli (Pisa).