Abstract
Let μ(λ):Δ→Δ be a measurable function depending real analytically on λ as element of L ∞(Δ) with μ(0)=0 and be the quasiconformal homeomorphic solution of the Beltrami differential equation Normalized by .In this article some equivaient conditions that guar antee that is stationary on the boundary for each λ in a neighborhood of are obtained. that is . In particular it is proven that has the following integral representation Using holomorphic motions it is obtained some applications to Teichmuller functions that are stationary on the boundary.
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