10 2. QUASICONFORMAL MAPPING S THEOREM 2.2. Let /i be a measurable function in a domain ft c C and suppose ||/i||oo 1- 77&en £/iere is a quasiconformal mapping g : Q — C whose complex Bel- trami coefficient is equal to fi almost everywhere. Moreover every WZo'c (fi) solution f to the Beltrami equation is of the form f(z) = F(g(z)) where F : g(Q.) — C is a holomorphic function. The main results of this paper are sharp generalizations of these two funda- mental theorems in the degenerate elliptic case. That is when ||/x||oo = 1- This follows and extends the pioneering work of David [33]. As discussed in the intro- duction, there is also related earlier work of Lehto on these more general problems, see [72, 73] where a number of the necessary estimates can be found. Let us now turn to a more general discussion.

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