On periodic Teichmüller disks of modular transformations

Abstract

We study the periodic Teichmuller disks of modular transformations. Especially, we prove that a parabolic modular transformation has either no periodic Teichmulluller disk or infinitely many periodic Teichmuller disks which can be chosen to cover infinitely many arithmetic Teichmuller curves in the Riemann moduli space Mg. Some related topics are also discussed.