A fiber bundle over BMO Teichmüller space

Abstract: We prove that the fiber space consisting of BMOA functions that are the logarithms of derivatives of conformal homeomorphisms of the unit disk onto bounded quasidisks forms a real-analytic disk bundle over the Bers embedding of the BMO Teichm\"uller space. For the VMO Teichm\"uller space, we show that the corresponding sub-bundle consisting of VMOA functions is real-analytically trivial.