English

Asymptotic Dirichlet problem for harmonic maps and conformal geodesics

Differential Geometry 2025-02-17 v3

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.

Keywords

Cite

@article{arxiv.2404.02895,
  title  = {Asymptotic Dirichlet problem for harmonic maps and conformal geodesics},
  author = {Yoshihiko Matsumoto},
  journal= {arXiv preprint arXiv:2404.02895},
  year   = {2025}
}

Comments

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

R2 v1 2026-06-28T15:43:16.543Z