Harmonic maps between ideal 2-dimensional simplicial complexes

摘要

We prove existence and regularity results for energy minimizing maps between ideal hyperbolic 2-dimensional simplicial complexes. The spaces in question were introduced by Charitos-Papadopoulos, who describe their Teichmuller spaces and some compactifications. This work is a first step in introducing harmonic map theory into the Teichmuller theory of these spaces.