Let G be a simply connected domain and let u(x,G) be its warping function. We prove that L p -norms of functions u and u -1 are monotone with respect to the parameter p. This monotony also gives isoperimetric inequalities ...

Themain result of this paper is analogues of the Schwarz lemma for the torsional rigidity and the conformal moment of inertia of simply connected domains. Moreover we obtain Schwarz-Pick type inequalities for these quantities ...