An application of the continuous Steiner symmetrization to Blaschke-Santaló diagrams

In this paper we consider the so-called procedure of Continuous Steiner Symmetrization , introduced by Brock in [F. Brock, Math. Nachr. 172 (1995) 25–48 and F. Proc. Indian Acad. Sci. 110 (2000) 157–204]. It transforms every open set Ω ⊂⊂ ℝ d into ball keeping volume fixed letting first eigenvalue torsional rigidity respectively decrease increase. While does not provide, general, a γ -continuous map t ↦ it can be slightly modified so to obtain -continuity for -dense class domains Ω, namely, polyhedral sets . This allows sharp characterization Blaschke-Santaló diagram torsion eigenvalue.