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Uniformizing surfaces via discrete harmonic maps

Ryokichi Tanaka, Tohoku University
Tuesday, April 30, 2019 - 1:30pm
PDL C-401
We show that for any closed surface of genus greater than one and for any finite weighted graph filling the surface, there exists a hyperbolic metric which realizes the least Dirichlet energy harmonic embedding of the graph among a fixed homotopy class and all hyperbolic metrics on the surface. We also give explicit examples of such hyperbolic surfaces as a refinement of the Nielsen realization problem for the mapping class groups. Joint work with Toru Kajigaya (Tokyo Denki University).
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