On the degenerate Beltrami equation

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

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)


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).

Original languageEnglish
Pages (from-to)875-900
Number of pages26
JournalTransactions of the American Mathematical Society
Issue number3
Publication statusPublished - 2005 Mar


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