A variational construction of the Teichmüller map

Chikako Mese
September 2004
Calculus of Variations & Partial Differential Equations;Sep2004, Vol. 21 Issue 1, p15
Academic Journal
Gerstenhaber and Rauch proposed the problem of constructing the Teichmüller map by a maximum-minimum approach involving harmonic maps. In this paper, we show that the Teichmüller map can be constructed by this variational characterization. The key idea is to consider a class of metrics on the target which include singular metrics and use the harmonic map theory in this setting.


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