ON THE EXTENSION OF QUASISYMMETRIC MAPS.

We show that an ε-power-quasisymmetric map f: A → Rn can be extended to a Cε-power-quasisymmetric map F: Rn → Rn if A ⊂ Rn satisfies a geometric thickness condition and ε is small enough. The constant C depends on c and n only. [ABSTRACT FROM AUTHOR]