On Locally Quasiconformal Teichmuller Spaces

2019/07/17 by Alastair Fletcher, Fletcher, Alastair, Zemin, Zhou
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1907.07409

openalex publication_date 2019/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a universal Teichmüller space for locally quasiconformal mappings whose dilatation grows not faster than a certain rate. Paralleling the classical Teichmüller theory, we prove results of existence and uniqueness for extremal mappings in the generalized Teichmüller class. Further, we analyze the circle maps that arise.

Related

• Universal Teichmuller Space
• Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives
• Distortion of quasiconformal mappings with identity boundary values
• Extremal maps of the universal hyperbolic solenoid
• A commentary on Teichmüller's paper "Verschiebungssatz der quasikonformen Abbildung" (A displacement theorem of quasiconformal mapping)