Asymptotic Dirichlet problem for harmonic maps and conformal geodesics

Abstract

The asymptotic Dirichlet problem for harmonic maps from the hyperbolic plane into conformally compact Einstein manifolds is used to give a holographic characterization of conformal geodesics on the boundary at infinity, in a way deeply inspired by a work of Fine and Herfray on renormalized area minimization.

25 pages. Substantial update, including title change. Discussion on renormalized energy is moved from the main text to the appendix