We will study the Douady-Earle barycentric extension of maps on $S^{n-1}$. We will show the extension is uniformly Lipschitz if the map is quas-iregular, which, in a sense, is a generalization of Schwarz lemma. Using the bound on the Lipschitz constant, we are able to construct a geometric limit of a degenerating sequence of rational maps on an $\R$-tree. This geometric limit as $R$-tree is a generalization of Ribbon $R$-tree construction for compactification of Blaschke products by Curt McMullen, and as an analogue of the Thurston compactification for the surface group studied by Morgan-Shallen, Bestivina, Paulin and Otal. Speaker(s): Yusheng Luo (Harvard)
Building: | East Hall |
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Event Type: | Workshop / Seminar |
Tags: | Mathematics |
Source: | Happening @ Michigan from Department of Mathematics, Complex Analysis, Dynamics and Geometry Seminar - Department of Mathematics |