Title: A construction of trivial Beltrami coefficients,
Abstract: A measurable function $\mu$ on the unit disk $\mathbb{D}$ of the complex
plane with $\|\mu\|_\infty<1$ is sometimes called a Beltrami coefficient. We
say that $\mu$ is trivial if it is the complex dilatation $f_{\bar z}/f_z$ of a
quasiconformal automorphism $f$ of $\mathbb{D}$ satisfying the trivial boundary
condition $f(z)=z,~|z|=1.$ Since it is not easy to solve the Beltrami equation
explicitly, to detect triviality of a given Beltrami coefficient is a hard
problem, in general. In the present article, we offer a sufficient condition
for a Beltrami coefficient to be trivial. Our proof is based on Betker's
theorem on Löwner chains.