On Locally Quasiconformal Teichmuller Spaces

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