Proper harmonic embeddings of open Riemann surfaces into $\mathbb{R}^{4}$

Antonio Alarcón; Francisco J. López

doi:10.4171/jems/1782

JournalsjemsOnline First

Proper harmonic embeddings of open Riemann surfaces into $R^{4}$

Antonio Alarcón
Universidad de Granada, Spain
Francisco J. López
Universidad de Granada, Spain

$Proper harmonic embeddings of open Riemann surfaces into $\mathbb{R}^{4}$ cover$

Download PDF

A subscription is required to access this article.

Abstract

We prove that every open Riemann surface admits a proper embedding into $R^{4}$ 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 this article

Antonio Alarcón, Francisco J. López, Proper harmonic embeddings of open Riemann surfaces into $R^{4}$ . J. Eur. Math. Soc. (2026), published online first

DOI 10.4171/JEMS/1782