On Blaschke–Santaló diagrams for the torsional rigidity and the first Dirichlet eigenvalue

We study Blaschke-Santal\'o diagrams associated to the torsional rigidity and first eigenvalue of Laplacian with Dirichlet boundary conditions. work under convexity volume constraints, in both strong (volume exactly one) weak at most form. discuss some topological (closedness, simply connectedness) geometric (shape boundaries, slopes near point corresponding ball) properties these diagrams, also providing a list conjectures.