Asymptotic stability of large energy harmonic maps under the wave map from 2D hyperbolic spaces to 2D hyperbolic spaces

Abstract

In this paper, we prove that the large energy harmonic maps from H2 to H2 are asymptotically stable under the wave map equation. This work is the last paper in a series of works [46,45,44], which together prove the asymptotic stability for all “admissible” harmonic maps of arbitrary size without any symmetry assumptions.