Uniformizing surfaces via discrete harmonic maps

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 give explicit examples of such hyperbolic surfaces through a new interpretation of the Nielsen realization problem for the mapping class groups.Comment: 31 pages, 5 figure

ケーラー多様体におけるラグランジュ部分多様体の変分問題

Tohoku University宮岡礼子課