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.
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