On the degenerate Beltrami equation

: Gutlyanskiǐ V., Martio O., Sugawa T., Vuorinen M.

: 2005

: Transactions of the American Mathematical Society

: 357

: 3

: 875

: 900

: 26

: 0002-9947

DOI: https://doi.org/10.1090/S0002-9947-04-03708-0

: http://api.elsevier.com/content/abstract/scopus_id:14844337558

We study the well-known Beltrami equation under the assumption that its measurable complex-valued coefficient μ(z) has the norm ∥μ∥ = 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. A uniqueness theorem is also proved when the singular set Sing(μ) of μ is contained in a totally disconnected compact set with an additional thinness condition on Sing(μ). © 2004 American Mathematical Society.