Barycentric extension and degenerating sequences of rational maps

Geometry & Topology
Event time: 
Tuesday, October 16, 2018 - 4:15pm
DL 431
Yusheng Luo
Speaker affiliation: 
Event description: 

We start by investigating the well-known Douady-Earle/Barycentric extension of maps on $S^n$ introduced by Douady and Earle in the 1980s. We prove a regularity result of the extension of its Lipschitz constant. The regularity result allows us to construct a geometric limit of dynamics on an $\mathbf R$-tree for the extension of a degenerating sequence of rational maps. The dynamics on $\mathbf R$-trees gives a natural compactification of marked hyperbolic components. We will compare this compactification with Thurston’s compactification of Teichmüller spaces.

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