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Computation and Generalizations of the Douady-Earle Extension
In collaboration with Clifford Earle and others, we have developed a computational approach to the conformally natural extension due to Douady and Earle. In the disk, their early method extends homeomorphisms of the boundary of the disk D to homeomorphisms of D. A more general setting, that arises quite naturally, are the degree 1 monotone maps ofthe circle; that result will be discussed together with the iterative algorithm that provides the extension. Some generalizations arise from the algorithmic approach; open questions will be mentioned.
Thursday, November 17, 2005, 245 Altgeld Hall, 4:00 p.m.
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