Abstract
We study the well-known Beltrami equation under the assumption that its measurable complex-valued coefficient μ ( z ) \mu (z) has the norm ‖ μ ‖ ∞ = 1. \|\mu \|_\infty =1. Sufficient conditions for the existence of a homeomorphic solution to the Beltrami equation on the Riemann sphere are given in terms of the directional dilatation coefficients of μ . \mu . A uniqueness theorem is also proved when the singular set Sing ( μ ) \operatorname {Sing} (\mu ) of μ \mu is contained in a totally disconnected compact set with an additional thinness condition on Sing ( μ ) . \operatorname {Sing}(\mu ).
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