We study the well-known Beltrami equation under the assumption that its measurable complex-valued coefficient mu(z) has the norm parallel tomuparallel to(infinity) = 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 mu. A uniqueness theorem is also proved when the singular set Sing(mu) of mu is contained in a totally disconnected compact set with an additional thinness condition on Sing(mu).
展开▼
