Integral means spectrum functionals on Teichmuller spaces

Abstract: In this paper, we introduce and study the integral means spectrum (IMS) functionals on Teichmuller spaces. We show that the IMS functionals on the closure of the universal Teichmuller space and on the asymptotic universal Teichmuller space are both continuous. During the proof, we obtain some new results about the universal asymptotic Teichmuller space. We also show that the integral means spectrum of any univalent function admitting a quasiconformal extension to the extended complex plane is strictly less than the universal integral means spectrum.