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We settle the problem of the uniqueness of normalized homeomorphic solutions to the nonlinear Beltrami equation $\bar {\partial }\ f(z)=\mathcal H(z,\ \partial f(z))$. It turns out that the uniqueness holds under explicit bounds on the ellipticity constant of the equation at infinity, but not in general.

Uniqueness of Normalized Homeomorphic Solutions to Nonlinear Beltrami Equations