Infinite energy harmonic maps from quasi-compact Kähler surfaces

Abstract

We construct infinite energy harmonic maps from a quasi-compact Kähler surface with a Poincaré-type metric into an NPC space. This is the first step in the construction of pluriharmonic maps from quasiprojective varieties into symmetric spaces of non-compact type, Euclidean and hyperbolic buildings and Teichmüller space.

Keywords

• harmonic maps
• quasi-compact kähler surfaces
• infinite energy
• non-positively curved