Proper harmonic embeddings of open Riemann surfaces into $\mathbb{R}^4$
Differential Geometry
2026-04-10 v3 Complex Variables
Abstract
We prove that every open Riemann surface admits a proper embedding into by harmonic functions. This reduces by one the previously known embedding dimension in this framework, dating back to a theorem by Greene and Wu from 1975.
Cite
@article{arxiv.2206.03566,
title = {Proper harmonic embeddings of open Riemann surfaces into $\mathbb{R}^4$},
author = {Antonio Alarcon and Francisco J. Lopez},
journal= {arXiv preprint arXiv:2206.03566},
year = {2026}
}
Comments
To appear in J. Eur. Math. Soc. (JEMS)