Local Holomorphic Families of Discs |
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1+ax 1+az Ahlfors Banach space Beltrami Bers fiber space calculation ch+1 ch+l Chapter cntl complex anti-linear complex linear composition lemma continuous converges D₁ D₁f(x define derivative estimates Df(x diffeomorphism differentiable direct sum dx dy equation equivalent Euclidean sense exp(f f is c² family of discs formula fractions lemma Hilbert transform Holder condition Holder estimates holomorphic family holomorphic function holomorphic map homeomorphism homotopy identity implies integrability condition invertible isomorphism J₂ J₂w linear transformation m+n+k measurable functions Mobius transformation neighborhood norm open set pointwise proceed by induction product complex structure product lemma Proof Proposition 2.20 pullback r₁ Riemann surface Subsection U₁ V₁ vector spaces Vekua w₂ zero ΖΕΔ