Quasiconformal and BMO-quasiconformal homeomorphisms

  • Jean-Pierre Otal

    Université Paul Sabatier, Toulouse, France
 Quasiconformal and  BMO-quasiconformal homeomorphisms cover
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Abstract

We expose a proof of the existence and uniqueness of homeomorphic solutions to the Beltrami equation ˉf=μf\bar \partial f = \mu \partial f a.e. in two cases. First, when the LL^\infty norm of μ\mu is <1<1: the homeomorphic solution is quasiconformal. Then when 11μ\frac 1{1-\vert \mu \vert } is bounded above by a function which is locally in BMO. In this case, the homeomorphic solution is BMO-quasiconformal.