On Holomorphic Contractibility of Teichmüller Spaces

Abstract

The problem of the holomorphic contractibility of Teichmüller spaces T(0,n) of the punctured spheres (n>4) arose in the 1970s in connection with solving algebraic equations in Banach algebras. Recently it was solved by the author. In the present paper, we give a refined proof of the holomorphic contractibility for all spaces T(0,n), n>4 and provide two independent proofs of holomorphic contractibility for low-dimensional Teichmüller spaces, which has intrinsic interest.

Keywords

• Teichmüller spaces
• Fuchsian group
• quasiconformal deformations
• holomorphic contractibility
• univalent function
• Schwarzian derivative