| dbo:abstract |
In mathematics, the measurable Riemann mapping theorem is a theorem proved in 1960 by Lars Ahlfors and Lipman Bers in complex analysis and geometric function theory. Contrary to its name, it is not a direct generalization of the Riemann mapping theorem, but instead a result concerning quasiconformal mappings and solutions of the Beltrami equation. The result was prefigured by earlier results of Charles Morrey from 1938 on quasi-linear elliptic partial differential equations. The theorem of Ahlfors and Bers states that if μ is a bounded measurable function on C with , then there is aunique solution f of the Beltrami equation for which f is a quasiconformal homeomorphism of C fixing the points 0, 1 and ∞. A similar result is true with C replaced by the unit disk D. Their proof used the Beurling transform, a singular integral operator. (en) |
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https://archive.org/details/complexdynamics0000carl http://www.math.qc.edu/~zakeri/papers/ahl-bers.pdf%7Cjournal=Nashr-e-Riazi%7Cvolume= |
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| rdfs:comment |
In mathematics, the measurable Riemann mapping theorem is a theorem proved in 1960 by Lars Ahlfors and Lipman Bers in complex analysis and geometric function theory. Contrary to its name, it is not a direct generalization of the Riemann mapping theorem, but instead a result concerning quasiconformal mappings and solutions of the Beltrami equation. The result was prefigured by earlier results of Charles Morrey from 1938 on quasi-linear elliptic partial differential equations. (en) |
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Measurable Riemann mapping theorem (en) |
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